
te^ i^.L Joy 



Book 



Copyright ]^^_ 



COPflRIGHT DEPOSIT 



Completion-Test 
LANGUAGE SCALES 



MARION REX TRABUE, Ph.D. 

Instructor in Educational Administration, Teachers College 
Columbia University 



TEACHERS COLLEGE, COLUMBIA UNIVERSITY 
CONTRIBUTIONS TO EDUCATION, No. 77 



PUBLISHED BY 

tlTeactersi College, Columbia Wini^Jtraitp 

NEW YORK CITY 

1916 



11 



Copyright, 1916, by Marion Rex Trabue 



PEB24I916 



^-t? 



©GI.A427008 



ACKNOWLEDGMENTS 

I wish to acknowledge here my indebtedness to those who have 
helped to make possible the completion of this study. Scores 
of teachers and school officers have cooperated with me in secur- 
ing completion-test papers from over thirteen thousand public 
school pupils, and I am glad to record my obligation to them. 
1 1 would be impossible to record here the names of all who have 
contributed thought and time to this investigation, but justice 
demands that I mention Professor E. L. Thorndike, whose exam- 
ple as an untiring scientific investigator and whose suggestive 
criticisms of this work as it has progressed have been of incalcu- 
lable value. It would also be unjust not to mention my wife, 
without whose encouragement, and actual assistance in the 
monotonous mechanical work of scoring the results, this report 
would have been impossible. 

M. R. T. 



Digitized by the Internet Archive 
in 2011 with funding from 
The Library of Congress 



http://www.archive.org/details/completiontestlaOOtrab 



CONTENTS 

PAGE 

I. Introduction 

Completion-Test Ability and Language I 

Improved Form of Completion Test 2 

II. Language Scale A 

1. History of Its Derivation 4 

2. Scale A, Itself 5 

3. Report of Scores Made on Scale A 6 

4. Criticism of Scale A ll 

5. Suggestive Results of Its Use 13 

Sex, Grade, and Age Differences 

III. Additional Language Scales 

1. Use of Short Scales 18 

2. Scales B and C 19 

3. Directions for Administering Tests 20 

4. Scales D and E 22 

5. Scales J and K 25 

6. Scales L and M 27 

IV. Calculation of the Difficulty of Test Sentences 

1. Variability of a Grade as the Unit 29 

2. Normal Surface of Frequency Assumed 30 

3. Scaling the Sentences of Scale A for Each Grade .... 35 

4. Measurement of the Distances Between Grades .... 41 

By Sentences, by Quartiles, and by Overlapping 

5. Selection of a Zero-Point for Completion-Test Ability ... 52 

6. Referring All Sentences of Scale A to Zero 54 

7. Estimation of the Difficulty of Other Sentences .... 61 

Appendix 

1. Correlations 77 

2. Scheme for Scoring Sentences 79 

3. Calculation of Medians 116 

4. Tentative Standard Scores in Language Scales B, C, D, and E 117 



INDEX OF TABLES 

NO. PAGE 

I. Distribution of Scores Made by Pupils of Each Elementary 

Grade in Language Scale A 8 

II. Distribution of Median Scores of Elementary Classes . . 9 

III. Distribution of Scores Made by Higher Grades in Scale A lo 

IV. Distribution of Scores Made by Sixth Grade Children . . 14 
V. Distribution of Scores Made by Twelve- Year-Old Children 15 

VI. Amounts of Improvement in Scale A Made in Six Months . 16 

VII. Steps and Intervals Between Steps on Scales B and C . . 20 

VIII, Steps and Intervals Between Steps on Scales D and E . . 24 

IX. Steps and Intervals Between Steps on Scales J and K . . 26 

X. Steps and Intervals Between Steps on Scales L and M . . 28 

XI. Score Made by Each Elementary Grade on Each Sentence of 

Language Scale A 36 

XII. Per Cent that Score Made by Each Elementary Grade is of 

Perfect Score for Each Sentence of Scale A .... 37 

XIII. P. E. Values Corresponding to Given Per Cents of the Nor- 

mal Surface of Frequency 38 

XIV. Difference Between 50 Per Cent and Per Cent of Perfect Score 

Made by Each Elementary Grade for Each Sentence of 

Scale A 39 

XV. P. E. Equivalent of Difference Between 50 Per Cent, etc. . 40 
XVI. Score and P. E. Equivalents for Each Sentence of Language 

Scale A in the Higher Grades 41 

XVII. P. E. Intervals Shown Between Consecutive Elementary 

Grades by Each Sentence of Language Scale A ... 42 
XVIII. Averages of Groups of Determinations of Inter-Grade Inter- 
vals, as Measured by Sentences of Language Scale A . 43 
XIX. P. E. Intervals Shown Between Consecutive Higher Grades 

by Each Sentence of Language Scale A 44 

XX. Score and P. E. Equivalents for Six Sentences in the 

Higher Grades 45 

XXI. Determination of the Quartile Intervals Between Elemen- 
tary Grades 46 

XXII. Determination of the Quartile Intervals Between Higher 

Grades 46 

XXIII. Percentages of Each Elementary Grade Distribution Lying 
Between Its Median and the Medians of Neighboring 

Grades, with P. E. Equivalents . 48 

vii 



viii Index of Tables 

NO. PAGE 

XXIV. Determinations of the Inter-Grade Intervals Obtained from 
Overlapping of Distributions of Scores on Language 

Scale A 49 

XXV. Percentages of Each Higher Grade Distribution Lying 
Between Its Median and the Medians of Neighboring 

Grades, with P. E. Equivalents 49 

XXVI. Distribution of Scores Made in High School Half Test . . 50 
XXVII. Three Determinations of the Interval Between Successive 

Grades 51 

XXVIII. Distances Above Zero of the Medians of Each School Grade 54 
XXIX. Location Above Zero of Each Sentence of Language Scale 

A for Each Elementary Grade 56 

XXX. Location of Each Sentence of Scale A for Each Higher 

Grade 57 

XXXI. Changes in Values Above Zero of Six Sentences by Use on 

Larger Numbers of High School Students 58 

XXXII. Determination of General Locations of Sentences • • • 59 

XXXIII. Final Values of Sentences in Scale A 60 

XXXIV. Score Made by Each Grade on Each Sentence of the Graded 

Series . . 62 

XXXV. P. E. Equivalents of Difference Between 50 Per Cent and 
Per Cent of Perfect Score Made by Each Grade for Each 

Sentence of the Graded Series 63 

XXXVI. Location Above Zero Shown by Each Grade for Each Sen- 
tence of the Graded Series 64 

XXXVII. Change of Location Above Zero Made in Each Sentence of 

the Graded Series by Its Inclusion in Language Scale A . 65 
XXXVIII. Estimated Location Above Zero of Each Sentence Given 

in the Graded Series Only 66 

XXXIX. Final Values of Sentences Given in the Graded Series Only 67 
XL. Score Made on Each Sentence of the Intermediate School 

Series 68 

XL I. Estimated Final Values of Sentences in the Intermediate 

School Series 69 

XLII. Score Made on Each Sentence of High School Short Test . 70 
XLIII. Estimated Final Values of Sentences in High School Short 

Test 71 

XLIV. Scores Made in High School Half Test 71 

XLV. Estimated Final Values of Sentences in High School Half 

Test 72 

XLVI. Scores and Estimates of Final Values for Second Grade 

Easy Test 72 

XLVII. Scores Made on Intermediate Grade Half-Test Sentences 73 



INDEX OF FIGURES 

NO. PAGE 

1. Comparison of the Inter-Grade Intervals Obtained on Scale A with 

Those Obtained Statistically 12 

2. Linear Projection of the Difficulty of the Sentences of Language 

Scale A 12 

3. Linear Projection of Language Scales B and C 20 

4. Linear Projection of Language Scales D and E 24 

5. Linear Projection of Language Scales J and K 26 

6. Linear Projection of Language Scales L and M 28 

7. Symmetrical Form of Distribution of Abilities to be Expected of 

Children in Any Given Grade 31 

8. Distribution of Scores Made by Second Grade Pupils on Scale A . 32 

9. Distribution of Scores Made by Third Grade Pupils on Scale A . 32 
ID. Distribution of Scores Made by Fourth Grade Pupils on Scale A . 32 

1 1 . Distribution of Scores Made by Fifth Grade Pupils on Scale A . . 33 

12. Distribution of Scores Made by Sixth Grade Pupils on Scale A . . 33 

13. Distribution of Scores Made by Seventh Grade Pupils on Scale A . 33 

14. Distribution of Scores Made by Eighth Grade Pupils on Scale A . 33 

15. Lower Half of a Normal Surface of Frequency 34 

16. Normal Surface of Frequency, with P. E. Distances from Median . 35 

17. Relations of Grade Distributions to Each Other 55 

18. Influence Allowed Various Parts of a Distribution in Determining the 

General Location of a Sentence 59 



COMPLETION-TEST LANGUAGE SCALES 

I 

INTRODUCTION 

This monograph is the report of an attempt to derive one or 
more scales for the measurement of abiHty along certain lines 
closely related to language. No attempt has been made to 
define "language" in any strict sense, and it is entirely possible 
that some persons may be able to speak the English language and 
perhaps to write it fairly well without being able to make a very 
high score on these scales. It may also happen that some indi- 
viduals will be found who score well on these language scales and 
are yet unable to quote a single rule of English grammar. On 
the whole, however, it will be found that ability to complete 
these sentences successfully is very closely related to what is 
usually called "language ability." 

Professor H. Ebbinghaus,^ who invented the completion-test 
method, characterized it as "a real test of intelligence. " It has 
been variously classified by psychologists, as a test of "imagina- 
tion, " as an "association test, " as a test of "memory, " and as a 
test of numerous other "faculties." As a matter of fact, the 
completion of incomplete sentences correlates remarkably well 
with almost any other measure of desirable qualities. / It would 
perhaps have been just as descriptive to have used the classifica- 
tion "general stand-out-ish-ness " suggested by Professor Hol- 
lingworth ;2 but the obvious dependence of the ability to complete 
sentences upon the ability to read and think about printed words, 
and the magnitude of the correlations obtained between the 
completion test and other tests of language ability seemed to 
justify the classification of the completion-test scales for educa- 
tional purposes as "language scales." 



^ H. Ebbinghaus: Ueber eine neue Methode zur Priifung geistiger Fahig- 
keiten und ihre Anwendung bei Schulkindern. Zeitschrift fur Psychologie, 
Vol. 13 (i897)_, pp. 401-459. 

^ H. L. Hollingworth and others: An Experimental Study of Self-Analysis, 
Estimates of Associates, and the Results of Tests. School and Society, Vol, 
II (1915). PP- 171-179- 



2 Completion-Test Language Scales 

One of the difficulties with the completion test has been that 
it was almost impossible to measure progress with it, because of 
the impossibility of finding two paragraphs of exactly the same 
difficulty. The story of a paragraph does not pass out of one's 
mind completely, and it is therefore not quite fair to say that 
better completion of the same paragraph at the second trial 
means improvement in ability. The scales presented in this 
study are made up of sentences dealing with a wide variety of 
subjects, none of which are very interesting in themselves, and as 
a rule they are forgotten comparatively soon. Because of this 
variety of subject matter and the careful gradation of the sen- 
tences, it will be possible to use the same scale upon the same 
children, after allowing a year or more for them to forget about 
it, without greatly invalidating the results. This will not be 
necessary, however, for Scales B, C, D, and E are for all practical 
purposes equal and interchangeable. Scales J and K are fairly 
well matched, and likewise Scales L and M differ very little in 
their difficulty. 

Having the tests arranged as steps on a scale with approxi- 
mately equal intervals between the steps offers several advan- 
tages over the paragraph-completion method. The individual 
being tested is not discouraged by having a task set for him which 
is beyond his powers, nor is he disgusted at having to do child's 
play. The first sentences are easy enough to encourage the 
youngest child who can read them, and the last sentences are 
hard enough to require thought of well trained persons. With 
these smaller sentence units it is also possible to get a more 
accurate judgment as to the quality of an individual's perform- 
ance, and the comparison of two such performances is much more 
valid. It is very much easier and more accurate to judge that a 
sentence is "right," "almost right," or "wrong" than it is to 
judge that a paragraph is 20 per cent, 35 per cent, or 70 per cent 
"right." The average teacher finds it almost impossible to 
assign paragraph-completion scores which are quite comparable 
to the scores that a trained psychologist would assign to the 
same paragraphs. Very few teachers will be found, however, 
who can not use the scales proposed in this monograph and, with 
the assistance of the suggested scheme for scoring given in the 
Appendix, secure results which may be compared directly with 
the results obtained by other teachers in other school systems. 



Introduction 3 

f 

Allowing the same amount of time to all pupils, and giving 
each pupil two credits for each sentence perfectly completed and 
one credit for each sentence almost perfectly completed, auto- 
matically takes account of the time spent upon the work, the 
quality of the work done, and the difficulty of the tests one is 
able to do. An elaborate system of weighting might be used, 
but the results would probably be no more accurate than those 
obtained by this simple method of scoring. The consecutive 
tests are so well graded that (except in Scale A, the use of which 
the writer does not recommend) there is only one chance out of 
four that any individual will complete a more difficult sentence 
without being able to complete those which precede it. If 
individual X can complete three sentences, individual Y four 
sentences, and Z five sentences on Scale D in the seven minutes 
allowed, we may feel fairly confident that X can complete the 
first three, Y the first four and Z the first five sentences, and that 
in ability to complete the sentences of Scale D, Z is as much 
better than Y as Y is better than X. In other words, with equal 
distances between steps, the same number of points score may 
be assigned for each step taken, without distorting the facts, for 
the score is cumulative. 



II 

LANGUAGE SCALE A 

I. History of Its Derivation 

During April, May, and June, 1914, the writer tested 855 
pupils in two public schools of New York City with a "prelim- 
inary list" of fifty-six completion-test sentences. The results 
obtained indicated that a few of the sentences of this preliminary 
list were so constructed as to have little value as completion 
tests for children, and that, after rearranging the sentences in the 
order of their difficulty, there were a few places in the list where 
gaps occurred between consecutive sentences. 

By throwing aside the poorly constructed sentences of the 
preliminary list, arranging the remainder according to their 
difficulty for the 855 children who had tried them, and attempt- 
ing to write other sentences to fill the gaps found in the prelimi- 
nary list, a second list of fifty-six sentences was prepared. This 
second list of fifty-six completion-test sentences will be referred 
to in this monograph as "The Graded Series."^ 

With the Graded Series of tests the writer tested, during the 
last two months of 19 14 and the first month of 191 5, over five 
thousand children in the public schools of New York and New 
Jersey. On the basis of these results, two sentences of the 
Graded Series were selected for each school grade, the two being 
selected for each grade which had proved to be just difficult 
enough to be done by about 50 per cent of the children in that 
grade. This list of twenty-four selected completion tests has for 
convenience been called "Language Scale A."^ Scale A there- 
fore contains two second grade sentences, two third grade sen- 
tences, and so on up through the eighth grade and high school, 
ending with two sentences which had proved so difficult that a 
rather small percentage of the first year college class had been 
able to complete them. 

^ This list was presented by the writer at the meeting of Section L of the 
American Association for the Advancement of Science, Dec. 31, 1914, at Phila- 
delphia. 

2 Scale A was reported in School and Society, April 10, 1915, under the title, 
"Some Results of a Graded Series of Completion Tests." 



Language Scale A 5 

2. Scale A, Itself 
On each line of dots, write the word which makes the best meaning 

ONLY ONE WORD ON EACH BLANK 

II 

X. The sky [?. blue. 

y. We are going 1>. school. 

I" 

X. The kind lady :..:!.... the poor man a dollar. 

y. The ....p..Ty.... plays -^to-h-. her dolls all day. 

IV ,, 

X. Time LZ often more valuable .......„::.... money. 

y. Boys and id/li.-^. soon become ...:....:.... and women. 

X. The poor baby .....Vlfj/A as if it were Ti.^.:!.!..!-— sick. ^ 

y. The ....>..\>.>^ rises x^:^..... the morning and ±:-aa.. at night. 

X. It is good to hear tyi- voice tl U. friend. 

y. She .....L£'^>.-^. if she will. 

X. The poor little ...t^zt^t has ...J.'^^L.: nothing to ....M...I.... ; he is hungry. 

y. The boy who ...SiW'kS.. hard ...'^.LL.... do well. 



X. Men ...v:.*--.— jnore ...1::.:.':^:':.. to do heavy work ...ILSa^x.. women. 

y. It is a ...j.ki-.j.l. task to be kind to every beggar . y>KSi«.. fe^f2. for 

money. 

I . I^ . .. f. 

*. Worry L-C^j.... never improved a situation but has r.. ... :;i.. made condi- 
tions ...l^.'S.i.-i... J , ' 
y. A home is ...Il.4:!\.— merely a place ....)£kkiL.. one ....U.v.."^':::.. live comfortably 



X. It is very ....klL.i.J... to become .^.SiWfAd. acquainted ....!..:: ....... persons who 

,....:. .a-.... timid. fl 'I'^f^^ 
y. To ..^.|j.i!iCyA... rnany things .. k:..->.*.'^.° ever finishing any of them Ic a 

hk&jsL habit. 

f^t.,.:^._.: ::, XI 

X. One's real ....'*fir.^.j 'appears ..l^hlcllTtf?^.. often in his ...:.§:i!:!:i^Hhan in his 

speech. > -t^ , \ 

y. When one feels drowsy and ....?..l......... it happens that he is 

. • .^i..:.... to fix his attention very successfully anything. 

X. The knowledge of Jy}:3:^l. .h?! use fire is .,. of 

-y important things known by but unknown .U animals. 

y. •*^h{::...L.. that are :......... to one by an ..'.-..., friend should be pardoned 

.....^i^33-ii.. readily than injuries done by one ...}i^L)^£:.. is not angry. 

! x;iii 

*. To .IV.^L'l^r... friends is always u.::...:..i.... the .,.; it takes. 

y. One ought to ...i.4-..W,... great care to i...il:.. the right ...^^!}::^ of 

.i..':.Lj-.::.;., for one who A&^-^!±i bad habits ..kh^J/k?. it ..}k:&i^.. to 
get away from them. ^ A^jLUUt 



6 Completion-Test Language Scales 

3. Report of Scores Made on Scale A 

During the months of April, May, and June, 191 5, over six 
thousand children and young people spent fifteen minutes each 
in an attempt to complete the sentences of Scale A, as shown 
above. In those cases where a third page of sentences was added, 
enough more time was allowed to enable each individual to have 
a reasonable amount of time for each sentence. The majority 
of the classes tested were in the schools of New York and New 
Jersey, although records were obtained from a number of classes 
in Illinois, Indiana, Michigan, Missouri, and Pennsylvania.^ 
The results from these other states indicated that there was no 
great difference in the abilities of children in the same grade in 
different states, so that the measurements here reported may be 
taken as fairly representative of conditions in general. 

The detailed scheme by which each sentence was scored will 
be found in the Appendix, but in order that the reader may under- 
stand what is meant by the score, a word of explanation will be 
given here. Each sentence which the pupil had the opportunity 
to complete was given a score of 2 if perfectly completed, a score 
of I if almost but not quite perfectly completed, and a score of o 
if not attempted at all or if imperfectly done. The child who 
successfully completed two sentences in Scale A would therefore 
receive a score of 4, or 2 points for each sentence. If he had com- 
pleted three sentences perfectly and a fourth very nearly per- 
fectly, his total score would be 7 points. In this way anyone 
who did all the twenty-four sentences of Scale A perfectly in 

^ In these cases it was impossible for the writer himself to give the tests, 
although there is every reason to believe that the results are fully comparable 
to those given by him personally. The classes chosen in these states were in 
each case chosen because of the principal's training and understanding of 
scientific testing, and detailed instructions were given each principal in order 
to secure exactly comparable results. All of the papers were scored by the 
same detailed scheme, which was prepared by the writer and will be found in 
the Appendix. All papers were scored either by the writer or by his wife, 
except in the case of some of the papers of the preliminary list on which some 
assistance was given by one other individual. 

In the New York and New Jersey classes the writer hired substitute teachers 
to assist him in keeping time and collecting papers. He would instruct these 
assistants and train them so that they knew just what to do. He would then 
go to a class room, explain the test to the children, start them to work, and 
leave one of these assistants to collect the papers while he went to another 
room, where the same procedure was followed. In this way he was able with 
three assistants to obtain records from a large number of children in a short 
time. In a few instances these trained assistants were allowed to take com- 
plete charge of the administration of the tests after they had become thor- 
oughly familiar with the process. 



Language Scale A 7 

fifteen minutes would receive a total of 48 points, which is the 
maximum possible score in Scale A. 

In addition to the six thousand individuals who tried Language 
Scale A in the form given above, I have gone through the records 
of the five thousand who tried the Graded Series, from which 
Scale A was selected, and have found the total score made by 
each individual in the twenty-four sentences of Scale A. The 
results from these two groups vary little and are combined in 
Table I, which shows the distribution of scores made by the 
pupils of each elementary school grade. Beginning at the lower 
left-hand corner, Table I indicates that a score of o was made by 
255 of the 1318 pupils in the second grade, by 19 of the 1437 pupils 
in the third grade, and by i of the 1463 pupils in the fourth grade. 
Table I not only shows the number of pupils in each grade who 
made each score, but it also shows the median score, or the score 
made by the middle pupil of the grade if all the pupils of the 
grade were arranged in order according to the ability each exhib- 
ited in this test. In addition. Table I gives the range of score 
that would be necessary in each grade to include half of all the 
children in the grade, and the quartile, which is half of the range 
of the middle 50 per cent and will serve as a useful measure of the 
variability. 



8 Completion-Test Language Scales 

TABLE I 

DiSTKIBUTION OP ScORES MaDE BY PuPILS OP EaCH ELEMENTARY GrADE 

IN Language Scale A 



Two points 


score given for each sentence perfectly completed 




Score 


Grade 
II 


Grade 
III 


Grade 
IV 


Grade 
V 


Grade 
VI 


Grade 
VII 


Grade 
VIII 


48 
















47 
















46 

















45 














... 1.. 


44 












... 2.. 


... 2.. 


43 












... 3.. 


... 1.. 


42 










... i.. 


... 2.. 
... 1.. 


... 4 . 


41 












... 7.. 


40 












... 4.. 


... 20.. 


39 










... 1.. 


... 7.. 
... 3.. 
... 6.. 
... 18.. 
... 22.. 
... 27.. 
... 42.. 
... 45.. 
... 49.. 
... 75.. 
... 63.. 
... 92.. 
... 95.. 
... 89.. 
...114.. 
... 98.. 
...105.. 
... 96.. 
... 81.. 
... 62.. 
... 59.. 
... 68.. 
... 42.. 
... 33.. 
... 21.. 
... 21.. 
... 7.. 
... 4.. 
. 3 


... 16.. 


38 










... 2.. 


... 38.. 


37 






... 1.. 


... 3,. 


... 2.. 
... 1.. 


... 25.. 


36 








... 28.. 


35 








... 1.. 


... 5.. 
... 10.. 
... 12.. 


... 47.. 


34 








... 1.. 


... 59.. 


33 










... 63 . 


32 








... 4.. 


... 12.. 
... 27.. 
... 20.. 
... 39.. 
... 48.. 
... 72.. 
... 70.. 
... 65.. 
...111.. 
...115.. 
...106.. 
... 97.. 
...105.. 
...100.. 
... 81.. 
... 76.. 
... 58.. 
... 47.. 
... 56.. 
... 42.. 
... 24.. 
... 15.. 
... 13.. 
... 7.. 
... 7.. 


... 79.. 


31 








... 5.. 


... 70.. 


30 






... 2.. 


... 5.. 
... 10.. 
... 22.. 
... 25.. 
... 41.. 
... 43.. 
... 55.. 
... 68.. 
... 96.. 
... 90.. 
...105.. 
...119.. 
... 99.. 
...105.. 
...107.. 
...106.. 
... 99.. 
... 81.. 
... 63.. 
... 41.. 
... 44.. 
... 19.. 
... 20.. 
... 12.. 
... 9.. 
... 5.. 


... 78 . 


29 






... 4.. 


... 89.. 


28 






... 2.. 


... 92.. 


27 




... 1.. 


... 6.. 
... 14.. 


... 88 . 


26 






...101.. 


25 




... 1.. 


... 21.. 
... 24.. 
... 29.. 
... 49.. 
... 48.. 
... 70.. 
... 66.. 
... 74.. 
... 68.. 
... 94.. 
... 87.. 
...108.. 
...100.. 
... 83.. 
... 90.. 
... 80.. 
... 72.. 
... 80.. 
... 62.. 
... 48.. 
... 35.. 
... 29.. 
... 7.. 


...108.. 


24 




... 2.. 


... 82.. 


23 




... 1.. 


... 64.. 


22 




... 14.. 


... 65.. 


21 




... 17.. 


... 51.. 


20 


... 1. . 


... 16.. 
... 21.. 
... 35.. 


... 47.. 


19 


... 3.. 


... 36.. 


18 




... 19.. 


17 


... 5.. 


... 39.. 
... 40.. 
... 59.. 
... 52.. 
... 64.. 
... 73.. 
... 94.. 
...103.. 
... 85.. 
...110.. 
...106.. 
...185.. 
... 88.. 
...142.. 
... 29.. 
... 35.. 
... 6.. 
... 19.. 


... 15.. 


16 


... 3.. 


... 10.. 


15 


... 5. . 


... 13.. 


14 


... 8.. 


... 3.. 


13 


... 12.. 


... 1.. 


12 


... 9.. 


... 1.. 


11 


... 24 . . 




10 


... 22.. 


... 2.. 

... 4. . 


... 1.. 


9 


... 34.. 


... 1.. 


8 


... 74.. 


... 1.. 


7 


... 47.. 


... 2.. 
... 2.. 


... 1 




6 


...190.. 




... 1.. 


5 


. . . 72.. 








4 


...367.. 


... 3.. 


... 1.. 






3 


... 31.. 


... 1.. 






2 


. ..135.. 


... 6.. 
... 3.. 


... 1.. 


... 1 






1 


... 21.. 











...255.. 


... 1.. 
























No. tested 


1318 


1437 


1463 


1507 


1454 


1456 


1427 






Median Score 


4.591 


8.986 


14.329 


18.389 


21.917 


25.272 


28.060 






25 Percentile 


2.396 
6.566 


6.217 
13.043 


10.284 
18.598 


14.975 
22 . 023 


18.142 
25.361 


21.580 
29.079 


24 338 


75 Percentile 


32.421 






Quartile 


2.085 


3.413 


4.157 


3.614 


3.610 


3.750 


4.041 







Medians and percentiles should not be worked out to the third decimal point in ordinary 
practice. Reporting the median to the nearest whole number or to the nearest tenth of a 
whole number will be better when dealing with Scale A, for reporting to the third decimal sug- 
gests a refinement of measurement to which Scale A can lay no claim, except in cases where 
large numbers of individuals have been measured, as in the case of Table I. 



Language Scale A 9 

For those interested in the measurement of classes, Table II 
has been prepared, showing the distribution of median class 
scores in the elementary grades. As would be expected, the 
median of the class medians is very nearly equal to the median 
score of all children tested in any given grade. 



TABLE II 

DiSTKIBTJTION OF MEDIAN ScORES MaDE BY ELEMENTARY SCHOOL CLASSES 

IN Language Scale A 



Score 


Grade 


Grade 


Grade 


Grade 


Grade 


Grade 


Grade 


II 


III 


IV 


V 


VI 


VII 


VIII 


48 
















47 
















46 
















45 
















44 
















43 
















42 
















41 
















40 
















39 
















38 
















37. 
















36 
















35 

















34 














'.'.'.' 2.'.'. 


33 














... 2... 


32 















... 1... 


31 












'.'."i'.V. 


... 3... 


30 












... 1... 


... 6... 


29 












... 4... 


... 4... 


28 












... 4... 


... 9... 


27 












... 3... 


... 5... 


26 








'.'.'.' i'.'.'. 


;'.;'i;;; 


...10... 


... 8... 


25 










... 6... 


... 5... 


...10... 


24 








'.'.'.' i'.'.'. 


... 6... 


... 5... 


... 5... 


23 








... 1... 


... 6... 


... 7... 




22 






'.'.'.'2.'.'. 


... 1... 


... 3... 


... 5... 




21 








... 6... 


... 5... 


... 3... 




20 






'.'.'.'1.'.'. 


... 4... 


...10... 


... 1... 




19 






... 4... 


... 7... 


... 8... 






18 








... 5... 


... 2... 






17 






'.'.'.' k'.V. 


... 8... 


... 2... 






16 




.'.'."i..".' 


... 1... 


... 5... 








15 




... 3... 


... 7... 


... 2... 








14 




... 1... 


... 6... 


... 2... 








13 




... 4... 


... 5... 


... 1... 








12 




... 5... 


... 2... 










11 


'.'.'.'.i'.'.'. 


... 2... 


... 5... 










10 


... 1... 


... 6... 


... 4... 










9 




... 3... 


... 2... 










8 


'.'.'.'1.'.'. 


... 3... 












7 


... 3... 


... 6... 


'.'.'.' 2.'.'. 










6 


... 3... 


... 6... 












5 


... 4... 


... 4... 












4 


...10... 


... 2... 












3 


... 2... 














2 


... 5... 














1 


... 2... 

















... 1... 














No. classes tested 


33 


45 


45 


44 


49 


49 


54 


Median of median scores 


4.6 


9.8 


14.4 


18.8 


21.5 


25.7 


27.8 



10 



Completion-Test Language Scales 



Table III gives facts similar to those of Table I, with regard 
to the higher grades in those school systems where it was possible 
to obtain results from the complete system including the high 
school. The group headed "College Graduates" was composed 

TABLE III 

Distribution of Scores Made by Higher Grades in Language Scale A 
(Complete System Group) 



Score 


Grade 
VIII 


Grade 
IX 


Grade 
X 


Grade 
XI 


Grade 
XII 


College 
Graduates 


48 














47 


















1. 






.. 5... 
..11... 
..14... 
..12... 
..12... 
..16... 
.. 9... 

. 4... 

.4... 

.7... 

. 4... 

. 4... 

. 4... 

. 1... 

. 3... 

. 2... 

. 1... 

'."x.'.'. 




46 










.. 1. .. 




. 1 

. 2 

. 3 

. 5 

. 2 

2 

7 

13 

14 

11 

5 

11 

10 

12 

6 

5 

4 

6 

5 

3 

5 

2 

2 




3. 




45 

44 

43 

42 

41 

40 

39 

38 

37 

36 

35 

34 

33 

32 

31 

30 

29 

28 

27 

26 

25 

24 

23 

22 


.... 2... 
.... 2... 
.... 8... 
.... 4... 

... 3.... 

...10.... 

...10.... 

...17.... 

...18.... 

...16.... 

...17.... 

...22.... 

...24.... 

...18.... 

...23.... 

...27.... 

...22.... 

...17.... 

... 7 




. 6... 

4... 

8... 

6... 
11... 

7... 

6.... 
11.... 
18.... 
12.... 
20.... 
13.... 
17.... 
19.... 
15.... 
21.... 
11.... 
19.... 
17.... 

5.... 

7 




.. 1... 
.. 2... 
.. 7... 
.. 5... 

.5... 

. 4... 

. 7... 

. 9.... 

.19.... 

. 7.... 

. 3.... 

.12.... 

.11.... 

. 8.... 

.13.... 

.16.... 

. 5.... 

.11.... 

. 8.... 

. 3.... 

. 2.... 

. 3.... 

. 1.... 

. 4 






.... 1. 
.... 6. 
.... 5. 
.... 3. 
.... 6. 
.... 4. 
.... 7. 
.... 8. 
.... 9. 
.... 6. 
.... 7. 

... 6. 

... 6. 

... 7. 

... 5. 

... 4. 

'.'.'.'2. 
... 4. 
... 1. 




21 


. . .15 




5 




. 1 


















20 


. . .10 




5 




. 1 


















19 


... 7 




4 






















18 


... 3 




3 






















17 


... 1 




1. .. 




. 1 


















16 


... 5 




1 






















15 


... 2 




1 






















14 










. 1 


















13 


... 1 


























12 


... 1 


























11 




























10 




























9 




























8 




























7 




























6 


















J 










5 




























4 




























3 




























2 




























1 









































































313 


273 


171 


136 


103 


114 






Median Score 


27.861 


30.147 


33.682 


35.727 


37.167 


42.812 


25 Percentile 

75 Percentile 


24.420 
31.797 


26.023 
34.486 


30.109 
37.908 


32.333 
39.077 


33.125 
40.812 


39.375 
45.107 


Quartile 


3 688 


4 2.^2 


3 SQ9 


3 372 


3.844 


2.8fifi 


















1 




1 









Language Scale A ii 

of graduate students in Educational Administration at Teachers 
College. This last group was used simply as a group superior to 
high school seniors. 

4. Criticism of Scale A 

It will be noticed as one glances up through the grades that 
each successive grade makes a higher score than the grade just 
previous and that the range of the middle 50 per cent likewise 
moves steadily upward. This is, of course, to be expected, al- 
though the relative amounts of progress between grades are 
unusual and need to be examined more carefully. The crude 
score intervals between grade medians are, according to Table I, 
roughly as follows: 



Grades 


II-III 


III-IV 


IV-V 


V-VI 


VI-VII 


VII-VIII 


Interval 


4.4 


5.3 


4.1 


3.5 


3.4 


2.8 



There is no good reason for thinking that greater progress is 
made between the third and fourth grades than between the 
second and third, and careful examination proves that this 
relatively large advance between the third and fourth grades is 
due to imperfections in Scale A. If it had been possible, in the 
selection of the sentences for Scale A, to select two sentences of 
exactly "median" or 50 per cent difficulty for each grade, and 
then if the pupils tested later had performed exactly as those 
tested previously, there would have been a distinct tendency 
toward the equalization of the score intervals between grades, 
although the intervals would still have decreased in passing to 
higher grades. As it happened, the second grade sentences were 
distinctly too easy (59%, 58%); the third grade sentences 
too hard (46%, 46%) ; and the fourth grade sentences were prac- 
tically 50 per cent sentences (50%, 54%). As a result, the 
third grade did not have as much of a chance to show superiority 
over the second as the fourth had over the third. 

In a later section of this study the relative distances between 
grades are calculated to be about as follows: 

Grades II-III III-IV IV-V V-VI VI-VII VII-VIII 

Interval 1 1.6 1.2 .9 .8 .8 .6 



1 The unit upon which these intervals are calculated is the P.E., or the 
median deviation from the median of a grade distribution. This is explained 
in greater detail in the section headed "Normal Surface of Frequency Assumed" 
(p. 30-35), but for the present it may be thought of as a rather accurate unit 
of measurement which has the same value in all grades. 



12 Completion-Test Language Scales 

Fig. I gives a graphic comparison of the relations of the med- 
ians of the various school grades tested, measured first by the 
crude score on Language Scale A and second by the average of 
three determinations of the P.E. intervals. 



, 1 A 




i- -l J, 






T, 






I 


(0 


'n' ■■/*■ '16 ■ la' lo: It 

1 i i 


'2*' 


«' 


It 

1,' 


M' -SS' M' '36' JB' '4-I)' 

i J. i i i 


■.4i' .■«' 44' «' 


fiitiB «► tl SaU ^ 




H 4. 5 


6 




7 


8 9 W 


II /? 



Fig. I. Comparison of the Inter-Grade Intervals Obtained from Crude Score 
in Scale A with Those Obtained Statistically. Each circle above the line 
represents the position of the median of a school grade distribution on the 
scale shown below the line. 

Although the relative positions of the grades are in many 
respects similar in the two projections shown above, the crude 
score on the Language Scale is clearly not sufficiently accurate 
to be used alone. An arrangement of the sentences of Scale A 
on a linear projection similar to the second in Fig. I shows how 
imperfectly Scale A is constructed. 

Sentence Na „ «•<» ., ,„ 

, ' ^ g , .-'g ^'^^ , ■-^'•^' , s-'g-^g f <^ $A PL-_M 

0.0 ( ij Zfi 9<0 M St<g &0 7^0 8.0 9,0 10,0 II.O I2U) 

RS.SC.U 

Fig. 2. Linear Projection of the Difficulty of the Sentences of Language 

Scale A. 

A perfect scale for any function as complex as that tested by 
language completion tests would be very difficult to construct, 
although the scales presented in the next section of this report are 
far superior to Scale A in some particulars. It would be very 
convenient to have a scale in which each step was perfectly 
defined and exactly one unit more difficult than the step preceding 
it, but to secure such a scale would require an enormous amount 
of time and labor, and the advantage gained over a scale which 
approximates those conditions would be slight. A glance at Fig. 2, 
however, shows that there would be great improvement in 
Language Scale A if another step were introduced between sen- 
tences 2 and II and if some of the sentences between 6 P.E. and 
9 P.E. were omitted. The positions of the various school grade 
medians on the crude score projection in Fig. i indicate the same 
difficulty in Scale A. 



Language Scale A 13 

5. Suggestive Results of Its Use 

In spite of the inequalities that occur in the steps on Language 
Scale A, it has shown some rather interesting possibilities. There 
is a very general conviction among teachers that girls have greater 
ability along language lines than boys. I have gone through my 
records of sixth grade children and tabulated the scores of 1224 
of them according to sex and age.^ The results are shown in 
Table IV. 

On the whole, it appears from Table IV that boys make a 
somewhat lower median score than girls in the same grade, 
although the difference is small and the amount of overlapping 
is enormous. A small sampling from the other elementary 
grades indicated that the same conditions hold true there, so the 
facts shown in Table IV may be taken as fairly typical. It is 
interesting to note that there is a rather distinct tendency for the 
older pupils in the grade to make lower scores than those younger. 
This suggests that teachers are possibly inclined to promote dull 
pupils because of their age and to retard the bright pupils be- 
cause of their youth. However that may be, Table V makes 
it pretty clear that ability counts for a great deal more than 
age in determining promotion. 

In view of all that has been said recently concerning the inabil- 
ity of teachers to judge the abilities of their pupils and to pro- 
mote them accordingly, the facts shown in Table V are rather 
surprising. To say that a child is twelve years old apparently 
signifies far less concerning his ability to complete sentences 
than to say that he is in the sixth grade. The variability of the 
sixth grade, if the quartile is taken as a measure, is only about 
73 per cent of the variability of the twelve-year-olds. The 
median score of each grade group of twelve-year-old children 
is remarkably near the median score shown in Table I for all 
children in that grade group. There is undoubtedly a very 
close relation between the criteria used by teachers in promoting 
pupils and the abilities required to complete mutilated sentences. 

To measure progress in individual pupils and classes should be 
one of the uses of a good scale. In one school where the writer 
had given the Graded Series in November, 1914, the superin- 



^ This tabulation was made before all of the results were available, and 
therefore the total number of sixth grade children in this tabulation. is smaller 
than the total shown in Table I. 



14 



Completion-Test Language Scales 



TABLE IV 
Distribution of Scores Made by Sixth Grade Children 





Girls 


All 
Girls 


Boys 


All 
Boys 






Score 


Age 


Age 


Both 

Sexes 




10 11 


12 


13 


14 


15 


16 


10 


11 


12 


13 


14 


15 


16 




48 


































47 






































46 






































45 






































44 






































43 






































42 


















..1 














.. 1 


. 1. 




41 






































40 






































39 










.1. 






. 1. 




. 1 












.. 1, 


.. 2. 




38 


... . 1. 












. 1. 




. 1 












.. 1. 


. 2. 




37 


... . 1. 




..1. 








. 2. 








. 1 








.. 1. 


.. 3. 




36 






..1. 








. 1. 






. 1 










.. 1. 


.. 2. 




35 


.1. . 1. 












. 2. 




. 1 


. 1 










.. 2 


.. 4. 




34 


.1. . 2. 


. 1. 


..1. 








. 5. 




. 2 


. 1 




-.1. 






.. 4. 


.. 9. 




33 


.2 


. 1. 










. 3. 




. 2 


. 5 










.. 7. 


.10. 




32 


... . 2. 


. 3. 


..2. 








. 7. 


.1 


. 2 


. 3 


. 1 








.. 7 


.14. 




31 


.1. . 2. 


. 6. 


..1. 


..1. 






.11. 


..2 


. 6 


. 6 


. 2 








..16. 


.27. 




30 


.1. . 4. 


. 4. 


..2. 








.11. 




. 3 


. 6 










.. 9. 


.20. 




29 


.3. .14. 


. 4. 


..1. 


..3. 






.25. 




. 6 


. 7 


. 2 


..2. 






..17. 


..42. 




28 


.2. . 7. 


. 1. 


.3. 


..3. 


.1. 




.17. 


..4 


.16 


.10 


. 7 


..2. 


..1 




..40. 


.57. 




27 


.4. .10. 


. 9. 


..6. 


.1. 


.1. 




.31. 


..3 


.11 


. 5 


. 7 


..2. 


.1 




..29. 


.60. 




26 


.2. . 8. 


. 4. 


..7. 


..2. 






.23. 


..3 


.12 


.11 


. 9 








.35 


58, 




25 


.1. . 6. 


. 7. 


..3. 


..1. 






.18. 


-.7 


. 7 


.12 


. 9 


..3. 


.1 




..39 


57. 




24 


.6. . 9. 


.12. 


..8. 


..7. 






.42. 


..9 


.10 


.17 


.10 


..2. 


..2 




..50. 


,92, 




23 


.3. . 8. 


. 9. 


..9. 


..fi. 


.2. 




.37. 


..9 


.17 


.18 


. 9 


.5. 


.1 




.59 


96, 




22 


.4. .11. 


.16. 


..4, 


..3. 


.1. 




.39. 


..5 


.10 


.18 


.10 


..5. 


..2 




..50. 


..89. 




21 


... . 4. 


. 9. 


..6. 


..3. 






.22. 


..4 


.12 


.14 


.16 


..5. 


..4 




..55. 


77. 




20 


.1. . 6. 


. 8. 


..7. 


..2. 






.24. 


..5 


.13 


.17 


.14 


..7. 






..56. 


.80. 




19 


.2. . 3. 


. 9. 


..7. 


.3. 


.2. 


.1. 


.27. 


.2 


.24 


.19 


. 8 


..2. 




..1. 


..56. 


.83. 




18 


.1. . 3. 


. 6. 


..6. 


.3. 


.1. 




.20. 


..2 


.11 


.12 


. 9 


..7. 


..1 




..42. 


62. 




17 


... . 3. 


. 6. 


.4. 


..2. 


.2. 




.17. 


..6 


. 6 


.11 


.10 


..3. 


..5 




..41. 


..58. 




16 


.1. . 1. 


. 2. 


..4. 


..1. 


.1. 




.10. 


..1 


. 6 


.16 


. 5 


..8. 


..2 




.38. 


.48. 




15 


... . 3. 


. 2. 


..1. 


..2. 






. 8. 


.1 


. 4 


.10 


. 8 


.2. 


..2 




.27. 


35. 




14 


... . 1. 


. 2. 


.4. 


..2. 






. 9. 


..2 


. 9 


. 7 


. 7 


.6. 


..2 


.1, 


.34. 


43. 




13 


.2 


. 5. 


.2. 








. 9. 


..1 


. 4 


. 2 


. 6 


..4. 


..4 


..2. 


.23. 


.32. 




12 


... . 1. 




..2. 


..1. 


.1. 




. 5. 




. 3 


. 6 


. 3 


.1. 


.1 




..14. 


.19. 




11 




. i. 


.1. 








. 2. 




. 1 


. 1 


. 6 


..1. 


.1 


.1. 


.11 


.13. 




10 


... . 1. 


. 1. 


..1. 








. 3. 


..i 


. 1 


. 3 


. 1 


..1. 






.. 7. 


10. 




9 


... . 1. 












. 1. 


..1 




. 2 


. 2 


.2. 






.. 7. 


8. 




8 








..1. 






. 1. 






. 2 


. 1 


..1. 






.. 4. 


. 5. 




7 








..1. 








. 1. 










.1. 






.. 1. 


2 




6 
























. 1 








.. 1. 


.. 1. 




5 






































4 






























.1. 


.. 1. 


. 1. 




3 


























.1. 






.. 1. 


.. 1. 




2 

1 






























.1. 


.. 1. 


.. 1. 











































No. tested. . 


38 113 


128 


9S 


48 


12 


1 


435 


7( 


) 20 


1 24 


3 m 


74 


3( 


) 7 


789 


1224 


MedianScore 2 


4.8 25.2 


22.8 


22.4 


23,2 


19.5 


19.5 


23.5 


23.4 


22. 


3 21. 


3 21.] 


18.9 


17. f 


) 13.3 


21.5 


22.4 


25 percentile 














19.9 

















17.7 


18.5 


75 percentile 














27.3 


25.3 


26.1 


Quartile . . . 














3.7 
















3.8 


3.8 



Language Scale A 



15 



TABLE V 

Distribution op Scores Made by Twelve- Year-Old Children 





Girls 


All 


Boys 


All 




Score 


School Grade 




School Grade 




Both 








Girls 






Boys 


Sexes 




III 


IV 


V 


VI 


VII 


VIII 


III 


IV 


V 


VI 


VII 


VIII 




48 
































47 
































46 .. 
































45.. 
































44 


























.. 2. 


.. 2, 


.. 2.. 


43 
























.. 1. 


.. 1. 


.. 2. 


..2.. 


42 










.. 1. 




.. 1. 
















.. 1.. 


41.. 












. .1. 


.. 1. 
















.. 1.. 


40 










.. 1. 


...1. 


.. 2. 










.. 1. 


.. 2, 


.. 3. 


..5.. 


39 










.. 2. 


...1. 


.. 3. 










.. 2. 


.. 1. 


.. 3. 


..6.. 


38 












...1. 


.. 1. 










.. 3. 


.. 2. 


.. 5. 


..6.. 


37 
























.. 2. 


.. 3. 


.. 5. 


.. 5.. 


36 








. 1. 


.. 3. 




.. 4. 








. 1. 


.. 2. 


.. 3. 


.. 6. 


..10.. 


35 








. 3. 


.. 4. 


...2. 


.. 9. 








. 3. 


.. 1. 


.. 3. 


.. 7. 


..16.. 


34 








. 3. 


.. 4. 


...2. 


.. 9. 








. 2. 




.. 3. 


.. 5. 


..14.. 


33 








. 4. 


.. 3. 


...3. 


..10. 








. 5. 


.. 5. 


.. 3. 


..13. 


..23.. 


32 








. 4. 


.. 7. 




..11. 








. 5. 


.. 6. 


.. 5. 


..16. 


..27.. 


31 








. 4. 


.. 6. 


...2. 


..12. 






. 3. 


. 1. 


.. 9. 


.. 3. 


..16. 


..28.. 


30 








. 5. 


.. 8. 


...4. 


..17. 








. 6. 


.. 8. 


,. 6. 


..20. 


..37.. 


29 








. 4. 


..10. 


...3. 


17. 







. 1. 


. 9. 


.. 4 


,. 6. 


..20, 


..37.. 


28 








. 5. 


.. 7. 




..12. 


.... 




. 1. 


. 9. 


.. 5 


, , 7. 


..22 


..34.. 


27 






..5. 


.13. 


.. 6. 


...2. 


..26. 






. 3. 


. 8, 


..16 


.. 3. 


..30. 


..58.. 


26 






..4. 


. 9. 


.. 4. 


...3. 


..20. 








.11. 


..13 


.. 3. 


..27. 


..47.. 


25 




..1. 


..1. 


. 5. 


..10. 


...T. 


..18. 




..1. 


. 5. 


.14. 


..24, 


.. 5. 


..49. 


..67.. 


24 






..3. 


.17. 


.. 3. 


...1. 


..24. 


.... 




. 3. 


.16. 


..18. 


.. 3. 


..40. 


..64.. 


23 






..2. 


.13. 


.. 3. 


.4. 


.22. 




..1. 


. 5. 


.19. 


..20 


.. 3 


..48. 


..70.. 


22 




2. 


.3. 


.14. 


.. 4. 




..23. 


.... 


..1. 


. 2. 


.19. 


..14. 


.. 3. 


..39. 


..62.. 


21 




. 1. 


..8. 


.13. 


.. 7. 




..29. 


.... 


..1. 


. 4. 


.15. 


..15. 




..35. 


..64.. 


20 




..3. 


..6. 


.12. 




...1. 


.22. 


.... 


..2. 


. 9. 


.23. 


.. 8. 


.. 3. 


..45. 


..67.. 


19 






..6. 


. 8. 


.. 6. 


...2. 


..22. 




..2. 


.11. 


.21. 


.. 9. 




..43. 


..65.. 


18 




..2. 


..4. 


. 6. 


.. 1. 




..13. 






. 8. 


.13. 


.. 8. 


.. 1 


..30. 


..43.. 


17 




2. 


..2. 


. 6. 


.. 2. 




..12. 


..1. 


..2. 


.15. 


.12. 


.. 8. 


.. 2. 


..40. 


..52.. 


16 




..3. 


.A. 


. 4. 


.. 3. 




..14. 


..2, 


..6. 


.11. 


.18. 


.. 4. 




..41. 


..55.. 


15 




..2. 


..9. 


. 5. 






..16. 




..3. 


. 8. 


.13. 


.. 6. 




..30. 


..46.. 


14 


..1. 


.4. 


..5. 


. 5. 


.. 3. 




..18. 




..7. 


.19. 


. 8. 


.. 4. 




..38. 


..56.. 


13 




..2. 


..5. 


. 5. 






..12. 


..2. 


..5. 


.11 


. 5. 






..23. 


..35.. 


12 


..1. 


..4. 


..5. 


. 1. 






..11. 


..3, 


3. 


.10 


. 5. 






..21. 


..32.. 


11 




, 3. 


..3. 


. 1. 






.. 7. 


..2, 


..3. 


. 5, 


. 2. 






..12. 


..19.. 


10 


..1. 


..3. 


..3. 


. 1. 






.. 8. 


..2. 


.1. 


. 6. 


. 3. 






..12. 


..20.. 


9 




5. 


..3. 








, 8. 


,.2 


2 


. 5 


. 2. 


.. 1. 




..12. 


..20.. 


8 


..1. 


..7. 


..1. 








.. 9. 


..2. 


..9. 


. 3. 


. 1. 






..15. 


..24.. 


7 




..2. 










.. 2. 


1. 


. fi. 


. 4, 








..11. 


..13.. 


6 
















..3. 


..2. 


. 1, 








.. 6. 


..6.. 


5 


..2. 


,1. 










.. 3. 


..1. 


.2. 


. 1. 








.. 4. 


..7.. 


4 


















1 










.. 1. 


.. 1.. 


3 .. .. 
































2 

1 
















..1. 


..1. 


. 1. 








.. 3. 


.. 3.. 


.. .. 


















1 










.. 1. 


.. 1.. 


















22 
10.5 


62 
12.9 


155 
16.3 


269 
21.6 










No. tested 


6 


47 


82 


171 


108 


34 


448 


217 


76 


801 


1249 


Median Score 


9.5 


12.6 


18.3 


23.4 


28.3 


30.0 


22,8 


24.7 


29.8 


21.4 


21.9 


25 percentile 














17.3 






16.3 


16.5 


75 percentile 














27.9 














26,1 


26.9 


Quartile 














5.3 














4.9 


5,2 



I6 



Completion-Test Language Scales 



TABLE VI 

Amounts of Improvement in Language Scale A Made in Six 
Months' Work in School 



Amount of 
Improvement 


Eight-Year-Old 
Boys Girls 


Twelve-Year-Old 
Boys Girls 


18 






17 


. ... 1 




16 


2 


2 


1... 


15 


1 


1 


1 




14 


1 


2 


1 


13 




.... 4 


3.... 


12 


2 




2 


11 


1 


3 


1... 


10 


1 


1 


7 


2 


9 


1 


.... 2 

....11 


5.... 


8 


1 


5 


13.... 


7 


1 


7 


.... 6 


4.... 


6 


3 


7 


10 


9.... 


5 


3 


3 


10 


6.... 


4 


5 


11 


.... 6 


5 


3 


6 


4 


.... 6 


6.... 


2 


7 


7 


.... 5 


6.... 


1 


1 


2 


.... 4 


5.... 





11 


4 


3 


4.... 


-1 




.. . 2 


4.... 


-2 




.... 2 


1.... 


-3 




.... 3 


1.... 


-4 








-5 




1 








No. tested 


44 


61 


84 


80 






Median 
Improvement 


3.5 


5.8 • 


6.1 


6.1 



Table VI indicates that ii boys and 4 girls in the eight-year-old group made exactly the same 
score in June as in November, while one boy and two girls made one point more in June than 
in November, etc. It is interesting to note that some of the twelve-year-old children actually 
made poorer scores in June than they had made in November. 



tendent gave Language Scale A in June, 1915. The mid-year 
promotions which intervened had distributed the class groupings 
so that it was impossible to measure the progress of classes. The 
writer, however, searched out the November records of a group 
of eight-year-old children and of a group of twelve- year-old 
children to determine what score each of these children had made 
on the twenty-four sentences of Scale A. This record for each 
individual was then compared with his June record in Scale A, 



Language Scale A 17 

and any change of score was recorded. Table VI shows the 
changes that were found. The superintendent had emphasized 
the language work throughout the year on account of the poor 
showing made in November, so that the amount of progress 
shown in Table VI is possibly somewhat larger than would 
ordinarily be found. 

As we have already seen, the steps on Scale A are not equal in 
length. An improvement of ten points score may therefore mean 
something entirely different to two individuals, one of whom 
improves from 5 to 15 and the other from 20 to 30. For this 
reason the facts shown in Table VI are of little value, except as 
an illustration of how improvement may be measured now that 
we have scales on which the consecutive steps are equal. 



Ill 

ADDITIONAL LANGUAGE SCALES 

I. Use of Short Scales 

Although Language Scale A has proved itself a rather useful 
instrument, it has seemed best to arrange a number of shorter 
scales in which the intervals between steps are more nearly 
equal. It often happens that an individual does not feel "at 
his best " on certain days and, whether his level of performance is 
actually lower or not, at such times he feels that it is an injustice 
to him to have his ability judged on the basis of his "off day" 
performance. Measurements of individuals made for the pur- 
pose of obtaining correlations between tests are more useful if 
made at two or more different times with equal tests, for such a 
procedure allows one to make some very desirable corrections for 
the attenuation due to chance inaccuracies in the measures. 
Evidence from two or more measurements of the same indi- 
vidual becomes cumulative and convincing, while a single meas- 
urement may be overlooked as not significant. In fact, the 
amount of difference between the two measurements will often 
be taken as a rough indication of the reliability of the measure- 
ments. For these and other reasons the writer recommends that 
in measuring individuals two short scales be used rather than one 
long scale. 

Although it will always be advisable to use more than one of 
the short scales when an accurate measurement of an individual 
is desired, a class may be measured fairly well by means of a 
single scale. The chance inaccuracies in the measurement of an 
individual, whereby a single measurement gives him credit for 
more or for less ability than he deserves, tend to be balanced by 
inaccuracies in the opposite direction from the measurements of 
other individuals when a group is being measured. Improve- 
ment in a class may be measured by comparing the median score 
made by the class on one scale with the median score made by the 
class at a later date on another scale of the same difficulty, or 
even better by comparing the total distribution on one scale with 
the total distribution on the other equal scale. 
i8 



Additional Language Scales 19 

2. Scales B and C 

Language Scales B and C are chosen entirely from the care- 
fully evaluated sentences of the Graded Series and the writer feels 
a great deal of confidence in them. Each of these two scales 
consists of ten steps or sentences, each step being about i P.E. 
above the previous step. Scale C, however, is on the whole 
about .4 P.E. more difficult than Scale B. These two scales are 
as follows: 

Write only one word on each blank. 
Time limit, seven minutes. 

Name 



LANGUAGE SCALE B 

I . We like good boys girls. 

6. The is barking at the cat. 

8. The stars and the will shine tonight. 

22. Time often more valuable money. 

23. The poor baby as if it were sick. 

31. She if she will. 

35. Brothers and sisters always to help other 

and should quarrel. 

38 weather usually a good effect one's spirits. 

48. It is very annoying to tooth-ache, often 

comes at the most time imaginable. 

54. To friends is always the it takes. 



Write only one word on each blank. 
Time limit, seven minutes. 
-" Name 



LANGUAGE SCALE C 

2. The sky blue. 

5. Men older than boys. 

12. Good boys kind their sisters. 

19. The girl fell and her head. 

24. The rises the morning and at night. 

30. The boy who hard do well. 

37. Men more to do heavy work women. 

44. The sun is so that one can not 

directly causing great discomfort to the eyes. 

53. The knowledge of use fire is of 

important things known by but unknown animals. 

56. One ought to great care to the right of 

, for one who bad habits it to 

get away from them. 



20 



Completion-Test Language Scales 



The exact difficulty of each sentence in Scales B and C, with 
the intervals between consecutive steps, is shown in Table VII. 

TABLE VII 
Steps and Intervals Between Steps on Scales B and C, 1 = P.E. 



Language Scale B 


Language Scale C 


Sent. No. 


Value 


Interval 


Sent. No. 


Value 


Interval 


1 


.96 


1.02 


2 


1.38 


1.14 


6 


1.98 


.96 


5 


2.52 


1.06 


8 


2.94 


1.32 


12 


3.58 


.89 


22 


4.26 


1.14 


19 


4.47 


1.22 


23 


5.40 


1.10 


24 


5.69 


1.26 


31 


6.50 


.92 


30 


6.95 


.90 


35 


7.42 


1.00 


37 


7.85 


1.10 


38 


8.42 


1.08 


44 


8.95 


1.10 


48 


9.50 


1.26 


53 


10.05 


1.12 


54 


10.76 




56 


11.17 





The same facts are shown graphically in Fig. 3. 

Scole B t «, e « 23 31 ■ 35 3» 



Scale C 



1 2 3 4 5 & 7 8 9 10 II 12 

Fig. 3. Linear Projection of Language Scales B and C, 

Exactly seven minutes of actual work should be allowed any 
individual on either of these two scales. In testing school chil- 
dren, the procedure outlined below should be carefully followed 
in order that all measurements may be exactly comparable. 

3. Directions for Administering Tests 
If the class to be tested is a fourth grade class or higher, oral 
explanations will be sufficient. Below the fourth grade it will 
be necessary to distribute to each pupil the following practice 



Additional Language Scales 21 

list, before allowing any pupil to see the scale with which he is 
to be measured. 

Practice Sheet 

Two and two are 

A boy is little, but a man is 

Girls and boys can run play. 

The boy has book. 

After passing one of these practice sheets to each child, make 
the following general explanations : 

I want to see if you can read what is printed on the little sheet of paper, and 
whether you can guess what words have been left out. Each little dotted 
line shows where a word was left out. If you can guess what word ought to 
be there, write it on the dotted line. Write just one word on each blank. 
Make each line say something. 

After making the above explanation, the teacher and the 
examiner should give assistance to any child who does not 
understand, seeing that each child learns what is expected. 

After the examiner is confident that each child has the correct 
idea of how to proceed, a copy of the scale to be used should 
be held up in full view of the entire class and the statement made 
that "This page is very much like the little sheet on which you 
have just been working, except that the last sentences on this 
sheet are very much harder." From this point the procedure 
is practically the same as that for the higher grades. 

In the fourth grade or above, or after the preliminary practice 
just described has been completed in a lower grade, the following 
oral explanation of the scale to be used should be made before 
distributing any papers : 

This sheet contains some incomplete sentences, which form a scale. This 
scale is to measure how carefully and rapidly you can think, and especially 
how good you are in your language work. 

You are to write one word on each blank, in each case selecting the word 
which makes the most sensible statement. 

You may have just seven minutes in which to sign your name at the top 
of the page and write the words that are missing. The papers will be passed 
to you with the face downward. Do not turn them over until we are all ready. 
After the signal is given to start, remember that you are to write just one 
word on each blank and that your score depends on the number of perfect 
sentences you have at the end of seven minutes. 

If there are no questions, the papers may then be distributed, 
taking care that no child looks at the printed side until there 



22 Completion-Test Language Scales 

is a paper upon the desk of each child and the following additional 
instructions have been given: 

After you have been working seven minutes, I shall say, "The time is up. 
All stop writing!" You will all please stop at once and lay aside your pens 
(or pencils). Now if you are all ready, you may turn your papers, sign your 
names and fill the blanks. 

Take note of the exact time at which the signal to start was 
given, allow exactly seven minutes, and give the command to 
stop writing. Collect all papers at once. It is very important 
that exactly seven minutes be allowed. A stop watch is the 
most satisfactory means of keeping the time on a test of this sort. 

Grade each paper according to the scheme shown in the Appen- 
dix of this monograph, and make a record of the total number 
of points made by each child, in order that the amount of prog- 
ress made by each pupil may be readily determined when the 
scale is used the second time. (It would be advisable not to 
use the same scale again until a year or more has passed. Use 
a different scale of the same difficulty.) 

To calculate the median score of a class follow the directions 
given in Section 3 of the Appendix. 

4. Scales D and E 

Language Scales D and E are practically of the same difficulty 
as Scales B and C. Scales D and E, however, each contain four 
sentences which were not a part of the Graded Series,^ and al- 
though these two scales will be found very satisfactory, it is 
entirely possible that the difficulty of any one of the eight 
sentences referred to may differ as much as .3 or .4 P.E. from the 
value I have assigned to it. As a matter of fact, the course of 
this investigation has shown that the difficulty of a test sentence 
is influenced rather markedly by the number and character of 
the sentences near it. This does not, however, invalidate the 
scale; it merely indicates that the final value of each step on a 
scale of this kind cannot be determined accurately until thou- 
sands of children of all grades have attempted the scale in its 
final form. Indeed, it is questionable whether the utilities 
added by knowing so accurately the final value of each step would 

' All sentences numbered from i to 56 were in the Graded Series and, as will 
be found from reading Chapter IV of this monograph, the difficulty of each of 
them has been very well defined. The difficulty of all sentences numbered 
above 56 has been estimated as carefully as possible. 



Additional Language Scales 23 

be of sufficient practical importante to pay one for the labor of 
making the determination. 

Language Scales D and E are as follows : 

Write only one word on each blank. 
Time limit, seven minutes. 

Name 



LANGUAGE SCALE D 

4. We are going „ school. 

76. I to school each day. 

II. The plays her dolls all day. 

21. The rude child does not many friends. 

63. Hard makes tired. 

27. It is good to hear voice friend. 

71. The happiest and contented man is the one lives a 

busy and useful 

42. The best advice usually obtained one's 

parents. 
51 things are satisfying to an ordinary than 

congenial friends. 
84 a rule one association friends. 



Write only one word on each blank. 
Time limit, seven minutes. 

Name 



LANGUAGE SCALE E 

73. I see you. Can you see ? 

75. Ice is cold, but fire is 

7. The kind lady the poor man a dollar. 

18. The best to sleep is at night. 

58. Children should many lessons from parents. 

25. The child the river was drowned. 

34. It is a task to be kind to every beggar for 

money. 
36. Worry never improved a situation but has made 

conditions 

52. When one feels drowsy and , it happens that he is 

to fix his attention very successfully anything. 

83. In order clearly at it is to 

artificial 

The difficulty of each sentence in Scales D and E is shown 
in Table VIII. 



24 



Completion-Test Language Scales 



TABLE VIII 

Steps and Intervals between Steps on Scales D and E. 1=P.E. 



Lang 


uage Scale D 


Language Scale 


E 


gent. No. 


Value 


Interval 


Sent. No. 


Value 


Interval 


4 


1.00 


.97 


73 


1.18 


.45 


76 


1.97 


1.34 


75 


1.63 


1.71 


11 


3.31 


1.09 


7 


3.34 


1.08 


21 


4.40 


1.14 


18 


4.42 


1.13 


63 


5.54 


1.13 


58 


5.55 


.77 


27 


6.67 


.97 


25 


6.32 


.99 


71 


7.64 


1.22 


34 


7.31 


1.01 


42 


8.86 


.92 


36 


8.32 


.97 


51 


9.78 


1.07 


52 


9.29 


1.26 


84 


10.85 




83 


10.55 





Fig. 4 represents the same facts in a graphic way. 



5cale D 


o 






re 







o 




C3 

o 






G 






71 












51 
O 






1 




1 






i 


3 


4 




5 




G 






7 






6 




9 






10 


II 


Scale E 




75 

G 


75 





7 





IS 

o 




Sfl 





25 






3* 








© 




U 






85 
O 


• ' 








' 








' 




' 






' 


















' 



I 3 4 5 6 7 89 10 

Fig. 4. Linear Projection of Language Scales D and E. 

It will be observed that Scale E is somewhat more irregular 
and has a slightly shorter range than Scale D, The lower end 
of Scale E is a bit more difficult than the lower end of Scale D, 
while Scale D is the more difficult in the upper ranges. In spite 
of these differences, these two scales may ordinarily be used as 
though they were equal to each other and to Scales B and C. 

The instructions given above for the administration of Scales 
B and C apply equally well to these two scales. 



Additional Language Scales 25 

5. Scales J and K 

Scales J and K are intended to measure the abilities of young 
people and adults rather than of children. The time to be al- 
lowed is exactly five minutes for each of the scales, although 
the general procedure described above for Scales B and C should 
be followed in their administration. The intervals between 
steps in these two scales are intentionally made long, the upper 
steps are very high, and there are no sentences easier than 4. P.E. 
Care should be taken not to confuse Scales J and K with any 
other scales, for each of these two is equal to the other only. 

Language Scales J and K are as follows : 

Write only one word on each blank. 
Time limit, five minutes. 

Name 



LANGUAGE SCALE J 

29. Boys and soon become and women. 

61. The are often more contented the rich. 

64. The rose is a favorite because of fragrance and 



41. It is very to become acquainted persons 

who timid. 

93. Extremely old sometimes almost as care as 



87. One's in life upon so factors it is 

not to state any single for failure. 

89. The future of the stars and the facts of history are 

now once for all, I like them not. 



Write only one word on each blank. 
Time limit, five minutes. 

Name 



LANGUAGE SCALE K 

16. The boy will his hand if plays with fire. 

57. Hot weather comes in the and weather _ the 

winter. 

28. The poor little has nothing to ; he is hungry. 

33. Very few people how to spend time and to the best 

advantage. 

82. One not, as a , attention uninter- 
esting things. 

90. To eat one is is a pleasure. 

86 they us not, nature's are _ „ 

and unchangeable. 



26 



Completion-Test Language Scales 



Table IX shows the values that were obtained for each sen- 
tence in Scales J and K. 

TABLE IX 
Steps and Intekvai^ between Steps on Scales J and K. 1 = P.E. 



Language Scale J 


Language Scale K 


Sent. No. 


Value 


Interval 


Sent. No. 


Value 


Interval 


29 


4.12 


1.73 


16 


4.15 


1.83 


61 


5.85 


1.17 


57 


5.98 


1.06 


64 


7.02 


1.35 


28 


7.04 


1.34 


41 


8.37 


1.16 


33 


8.38 


1.18 


93 


9.53 


1.22 


82 


9.56 


1.23 


87 


10.76 


1.56 


90 


10.79 


1.86 


89 


12.31 




86 


12.65 





Fig. 5 is a linear projection showing the positions of each 
sentence of Scales J and K on the P.E. scale. 



5co 


e J 




«» 




0- 


S 


4t 




?* 




w 


I' 





1 


I 3 


4 


5 


e 


7 


8 


■S 




10' 


II 


!£■ I.i 


S« 


eK 




K 




57 


2S 


■ '^ 




»i 




? 


•e' 



I 2 3 4 5 6 7 a 9 10 II 12 13 

Fig. 5. Linear Projection of Language Scales J and K. 

The value obtained for each sentence in Scale K is remarkably- 
near the value obtained for the corresponding sentence in Scale 
J. The possibility that some of these values may shift when 
tried out on thousands of individuals is, however, even greater 
than in the case of Scales D and E. The values given in Table 
IX are nevertheless the most accurate obtainable at present 
and may be used with confidence until more exact values have 
been established. Scales J and K are unquestionably the most 
equally matched pair of completion tests for measuring young 
people and adults that have yet been obtained in the English 
language. 



Additional Language Scales 27 

6. Scales L and M 

For the measurement of smaller differences in the abilities 
of secondary school pupils, I have arranged Scales L and M, 
which begin at about 7 P.E. and progress by relatively small 
steps to over 11 P.E. These are also five-minute tests. It is 
believed that they will be found very valuable to secondary 
school teachers and others interested in the abilities of young 
people. 

The sentences composing Language Scales L and M are given 
below. 

Write only one word on each blank. 
Time limit, five minutes. 

Name 



LANGUAGE SCALE L 

60. Children are rude not easily win friends. 

66. Plenty exercise and air healthy 

and girls. 
70. In to maintain health, one should have nourishing 



65 happiness can not be with money. 

32. One's do always express his thoughts. 

92. To to wait, after having to go , very 

annoying. 

78. It is sometimes to between two of action. 

97. One can do his at one while of 

another. 

Write only one word on each blank. 
Time limit, five minutes. 

Name 



LANGUAGE SCALE M 

67. One can not foretell will happen in the 

59. The dog a useful because his intelligence 

and faithfulness. 
95. Many people their health because do not the 

of hygiene. 

79. Nothing can one's happiness eflfectively than a guilty 



45. To many things ever finishing any of them a 

habit. 

91. The seems and dreary a discouraged 

55 that are to one by an : friend should be par- 
doned readily than injuries done by one is not 

angry. 

88. It is that a full-grown man should _ a ghost _ he 

is 



28 



Completion-Test Language Scales 



Table X shows the values which have been obtained for each 
sentence in Scales L and M. 

TABLE X 
Steps and Intervals between Steps on Scales L and M. 1=P.E. 



Language Scale L 


Language Scale M 


Sent. No. 


Value 


Interval 


Sent. No. 


Value 


Interval 


60 
66 
70 
65 
32 
92 
78 
97 


6.83 
7.40 
7.91 
8.38 
8.91 
9.71 
10.14 
11.11 


.57 
.51 
.47 
.53 
.80 
.43 
.97 


67 
59 
95 
79 
45 
91 
55 
88 


6.93 
7.46 
7.94 
8.48 
9.04 
9.88 
10.19 
11.14 


.53 
.48 
.54 
.56 
.84 
.31 
.95 



Fig. 6 shows the positions of all sentences in Scales L and M. 



S«fe. 1 










g 


,n 


o 




G 




)J 




i i 


2 5 


i 


5 


6 


7 




8 




9 


10 


II 


12 


Scale 'f1 










tr 


» 


« 


't 


«$ 




IS 





12 3 4 5 6 7 ,a 9 JO /I 

Fig. 6. Linear Projection of Language Scales L and M. 



Note: The scales described in this chapter, together with the Practice Sheet 
shown on page 2i, may be purchased in any quantity from the Teachers Col- 
lege Bureau of Publications. 



IV 

CALCULATION OF THE DIFFICULTY OF TEST 
SENTENCES 

I. Variability of a Grade as the Unit 

The comparison of adjectives is a device used by all people 
to denote different amounts of qualities. When one makes the 
judgment that John is "brighter" than Joe, he has made a rough 
measurement of the amount of the quality termed "brightness" 
possessed by these two boys. If everyone knew John and Joe 
and their relative brightness, and if these two boys maintained 
exactly the same degrees of that quality from the present time 
forward, John and Joe might serve as a rough scale for brightness. 
It would then be possible to say that James has "the brightness 
of John" with some assurance of being understood. The diffi- 
culty with such an arrangement is that John and Joe both change 
in brightness and at different rates. It is also impossible for 
everyone to know these two boys, and therefore they cannot 
be of very wide service as a brightness scale. Any scale that is 
to be of much service must be built of units the amounts of which 
remain constant and in such form that they can be readily 
examined by anyone interested or verified by any competent 
person. 

It would be possible to build up a completion-test scale by 
merely selecting a series of sentences which the majority of a 
group of people agreed upon as arranged in the order of their diffi- 
culty. Or, one might select as a scale a series of sentences which 
had been tried upon a group of children and found to be so ar- 
ranged in the order of their difficulty that each consecutive sen- 
tence was correctly completed by just lo per cent of the group less 
than had completed the previous sentence. Such scales would no 
doubt be much more useful than an entirely ungraded series 
of sentences. Unless the above scales were based upon a firmer 
foundation than I have indicated, however, it would perhaps 
be found that a second group of judges would disagree with the 
first group in regard to a few of the sentences, and that a second 

29 



30 Completion-Test Language Scales 

group of children would show percentages entirely different 
from the first, possibly to the extent of showing no more than 20 
per cent difficulty between the hardest and the easiest sentences 
in the series, which with the previous group had a range of 100 
per cent. There is need for some less changeable unit than uncer- 
tain majorities or percentages of variable groups. 

One of the most constant things about a variable fact is the 
amount of its variability. One's accuracy as a judge of any 
quality remains fairly constant, and the accuracy of one group 
of judges very nearly equals the accuracy of any other similarly 
chosen group. 

The variation in the abilities of the children in one group is 
about equal to the variation in the abilities in any other group 
of children chosen in the same way. Teachers select their 
brightest pupils for promotion and refuse to promote the dullards. 
Now the abilities of teachers to make this selection is about the 
same in one school system as it is in another, and about the same 
in eighth grade teachers as it is in second grade teachers. As a 
result, one school grade may differ quite markedly from another 
in ability and yet the amount of variability in one will be very 
nearly equal to the amount of variability in the other. If one 
desires to make a scale for use in all grades, then, it would seem 
desirable to use some measure of the variability of a grade as 
the unit, since this is at once common to all grades and only 
slightly variable in itself. 

2. Normal Surface of Frequency Assumed 

Before choosing any particular measure of the variability of 
a grade to be used as a unit of measurement, it will be valuable 
to discover how the "completion-test ability" is distributed in 
each grade. If this ability is distributed in the same way as 
the abilities by which teachers judge to what grade a child belongs, 
we should expect to find most of the children in any given grade 
clustered about the average or median for that grade. We 
should not expect to find that teachers always make perfect 
judgments as to promotions, but we should expect to see fewer 
large errors than small ones. In short, we should expect to find 
the abilities of the children in any given grade distributed sym- 
metrically on each side of the average, as shown in Fig. 7. 



Calculation of the Difficulty of Test Sentences 31 




Very Good 



Fig. 7. Symmetrical Form of Distribution of Abilities to be Expected 
of Children in Any Given Grade. 

The height of the curve above the base-line indicates the number of 
individuals in the class having the ability shown on the base-line scale. 
Each individual is represented by an equal amount of the total area 
inclosed by the curve and the base-line. 

Assuming that Language Scale A is a reasonably valid meas- 
uring instrument for the completion-test ability, Figs. 8 to 14 
show how this ability was distributed in the 1400 children of 
each elementary grade tested by the writer.^ Except in the 
second and third grades,^ the curves are remarkably symmetrical 
and regular, conforming on the whole to the general character- 
istics of the normal surface of distribution shown in Fig. 7.^ All 
the evidence at hand leads us to believe that the distribution 
of the abilities measured by the completion test conforms to 
this shape in each grade, and it will therefore be assumed through- 
out the remainder of this study. 

Assuming the normal surface of frequency, then, the Median 
Deviation or P.E. from the median will be the most convenient 
measure of the variability to use as a unit. Of course one might 
use the distance between the best and the poorest individuals 
in the class as a measure of the variability, but this would give 
such a large unit that the scale would be practically useless as 
a measure of small differences. Another reason for not using 
the extreme range of the distribution as a measure is the fact 
that the few very poor individuals and the few very good indi- 
viduals in each grade would have more influence over the size 
of the unit than all the hundreds of average children in the grade. 

^ The data upon which Figs. 8 to 14 are based are shown in Table I. 

* The excessive height of the columns for scores of o, 2, 4, 6 and 8 in the 
second and third grade figures is due to the peculiarities of the method of 
scoring, in that 2 points score were given for each perfect sentence and i point 
for each partially perfect sentence. The children in these lower grades as a 
rule either get the sentence perfect or not at alh 

' This fact in itself is not conclusive proof that completion-test ability is 
distributed according to the normal surface of distribution. Better proof 
is found in the fact that if this assumption is made the results that follow are 
in such close accord with known facts. 



32 



Completion-Test Language Scales 



m 



® Median Score 

*■ Each area of Ifiis size represents 

the score of one pupil on Sco/e A 



u -^ ' — ■ — ' I — t . ■ 

Fig. 8. Distribution of Scores Made by Second Grade Pupils on Scale A. 




'o- ■■■[■■■ ■f~' (j- ■ 2^.'^ ..,.,.- -jj- ^- ■ - ■ 4j- >••.-. •^. 

Fig. 9. Distribution of Scores Made by Third Grade Pupils on Scale A. 




Fig. 10. Distribution of Scores Made by Fourth Grade Pupils on Scale A 



Calculation of the Difficulty of Test Sentences 33 




Fig. II. Distribution of Scores Made by Fifth Grade Pupils on Scale A. 



Fig. 12. Distribution of Scores Made by Sixth Grade Pupils on Scale A. 




Fig. 13. Distribution of Scores Made by Seventh Grade Pupils on Scale A. 




Fig. 14. Distribution of Scores Made by Eighth Grade Pupils on Scale A, 



34 Completion-Test Language Scales 

The median deviation is the median amount of deviation, 
whether the deviations are above the median of the distribution 
or below. If all the children in the grade were arranged in order 
according to their distance from the median along the base-line 
scale, we might begin at the median and count out just one half 
of the children. The distance along the base-line covered in 
counting out half of the children would be the median deviation. 




Fig. 15. Lower Half of a Normal Surface of Frequency. 

Fig. 15 shows the lower half of a normal surface of frequency, 
with a line drawn perpendicular to the base in such a way as to 
cut off just one half of the area below the median. Half of the 
deviations represented by the total area shown are greater than 
line BD and half of them are less than line BD. BD is therefore 
the median deviation from the median, or the P.E., as it will 
be called for convenience in this study. 

Since the normal surface of distribution is perfectly symmet- 
rical, the area ABC shown in Fig. 15 represents just one half 
or 50 per cent of all the individuals represented by the total 
surface. Since area DBCE is just one half of area ABC it must 
contain one fourth or 25 per cent of the total number of indi- 
viduals. If one draws a line perpendicular to the base at a 
point I P.E. below the median of a normal surface of distribution, 
he will always divide the lower half of the distribution into two 
equal parts, each of which contains 25 per cent of the total dis- 
tribution. Drawing a line i P.E. above the median would like- 
wise divide the upper half of the distribution into two equal 
parts, each containing 25 per cent of the total area. 

The characteristics of a normal surface of distribution have been 
very carefully worked out. We know that the middle 50 per cent 
of any such surface is contained within the limits — i P.E. and 
-fi P.E. We know that if we start from the median of the dis- 
tribution and go I P.E. in either direction, a perpendicular line 



Calculation of the Difficulty of Test Sentences 35 




Fig. 16. Normal Surface of Frequency, with P.E. Distances from Median. 

to the base at that point would so divide the distribution that 
25 per cent of all frequencies would lie between that line and the 
median; if we pass on to a point 2 P.E. from the median, 41.13 
per cent of the cases would lie between the perpendicular and the 
median; at 3 P.E. from the median, 47.85 per cent of all cases 
are between the perpendicular and the median; and at 4 P.E. 
from the median, 49.65 per cent of the surface lies between the 
perpendicular and the median. Theoretically, the curve and 
the base-line do not meet but continue to approach each other as 
the distance from the median becomes greater. For practical 
purposes, however, we may consider that they meet at about 
4.6 P.E. from the median, for a perpendicular drawn here cuts 
off only 0.1 per cent of all the surface. 

3. Scaling the Sentences of Scale A for Each Grade 

Having adopted the P.E. of a grade as the unit of measure- 
ment, and having assumed that the normal surface of frequency 
represents the distribution of completion-test ability in any 
given grade, we may now attempt to arrange our sentences upon 
a P.E. scale for each grade. 

Table XI gives the total number of points score made in each 
elementary grade upon each sentence of Language Scale A, and 
the score that would have been made on any given sentence if 
every child in a grade had succeeded in completing it perfectly. 

Table XI indicates that Sentence No. 2, "The sky 

blue," was given 1798 points out of a possible 2636 in the second 
grade, 2597 out of a possible 2874 points in the third grade, etc. 
Turned into per cents, sentence No. 2 made 68.21 per cent of 
the total score possible for it in the second grade, 90.36 per cent 
in the third grade, etc. Since the number of children tested was 
different in each grade, it will be necessary thus to reduce all 
scores to percentages in order that the surfaces of distribution 
may all be of the same area. The scores shown in Table XI are 
given in percentages by Table XII. 



36 Completion-Test Language Scales 

TABLE XI 

ScoKE Made by Each Elementary Grade on Each Sentence of 
Language Scale A 



Sentence 
No. 


Grade 
II 


Grade 
III 


Grade 
IV 


Grade 
V 


Grade 
VI 


Grade Grade 
VII VIII 


Graded Scale A 
Series 

2 2x 

4 2y 

7 3x 

11 3y 

22 4x 

29 4y 

23 5x 

24 5y 

27 6x 
31 6y 

28 7x 

30 7y 
37 8x 
34 By 
36 9x 
43 9y 
41 lOx 
45 lOy 
49 llx 

52 lly 

53 12x 

55 12y 

54 13x 

56 13y 


1798 

1834 

675 

568 

*131 

192 

*85 

*97 

*49 

*30 

*29 

*12 

*3 

*6 


2597 

2660 

1594 

1612 

714 

961 

689 

554 

487 

384 

258 

235 

61 

135 

6 

2 

3 

3 


2760 

2813 

2247 

2274 

1655 

1787 

1313 

1078 

967 

999 

663 

676 

347 

431 

51 

35 

94 

24 

3 

8 

1 

2 

3 


2884 

2957 

2668 

2704 

2381 

2470 

1881 

1775 

1329 

1317 

1090 

1105 

652 

753 

170 

168 

293 

93 

33 

18 

12 

11 

5 

3 


2752 

2865 

2750 

2747 

2568 

2650 

2150 

2131 

1542 

1721 

1477 

1455 

1027 

1181 

439 

455 

550 

241 

111 

71 

36 

25 

17 

11 


2825 

2885 

2854 

2806 

2797 

2766 

2405 

2408 

1833 

1950 

1790 

1775 

1464 

1525 

916 

917 

925 

432 

379 

290 

120 

108 

45 

35 


2766 

2818 

2801 

2791 

2781 

2790 

2528 

2565 

1943 

2050 

1925 

1987 

1573 

1771 

1244 

1272 

1280 

749 

695 

580 

302 

242 

141 

103 


No. tested 


1318 


1437 


1463 


1507 


1454 


1456 


1427 








*1029 














Perfect Score 


2636 


2874 


2926 


3014 


2908 


2912 


2854 








*2058 















A sentence like No. 36, which no one of the 131 8 children in 
the second grade was able to complete, is very evidently too 
difficult for second grade pupils. Just how much too difficult it 
is we do not know, but if we assume the normal surface of fre- 
quency we know that it is more than 4.6 P.E. above their median, 
for if it were nearer to the second grade median than that dis- 
tance, it would probably have received a score in this grade. As it 
is, the entire surface of the second grade distribution lies below 
sentence No. 36. A sentence receiving a score of 25 per cent in the 
second grade would be just 25 per cent or i P.E. too difficult for 



Calculation of the Difficulty of Test Sentences 



37 



TABLE XII 



Per Cent that Score Made by Each Elementary Grade is of Perfect 
Score for Each Sentence op Language Scale A 



Sentence 


Grade 


Grade 


Grade 


Grade 


Grade 


Grade 


Grade 




No. 


II 


III 


IV 


V 


VI 


VII 


VIII 


2 


2x 


68.21 


90.36 


94.32 


95.68 


94.64 


97.01 


96.92 


4 


2y 


69.57 


92.55 


96.14 


98.19 


98.52 


99.07 


98.74 


7 


3x 


21.82 


55.46 


76.79 


88.52 


94.57 


98.01 


98.14 


11 


3y 


21.55 


56.09 


77.72 


89.71 


94.46 


96.36 


97.79 


22 


4x 


6.37 


24.85 


56.63 


78.99 


88.33 


96.05 


97.44 


29 


4y 


7.29 


33.44 


61.07 


81.95 


91.13 


94.99 


97.76 


23 


5x 


4.13 


23.98 


44.87 


62.41 


73.93 


82.59 


88.58 


24 


5y 


4.72 


19.28 


36.85 


58.89 


73.28 


82.69 


89.88 


27 


6x 


2.39 


16.95 


33.05 


44.09 


53.03 


62.95 


68.08 


31 


6y 


1.46 


13.36 


34.15 


43.70 


59.18 


66.96 


71.83 


28 


7x 


1.41 


8.98 


22.66 


36.17 


50.79 


61.47 


67.45 


30 


7y 


.59 


8.18 


23.11 


36.67 


50.03 


60.95 


69.62 


37 


8x 


.15 


2.12 


11.86 


21.63 


35.32 


50.27 


55.12 


34 


8y 


.29 


4.70 


14.73 


24.98 


40.61 


52.37 


62.05 


36 


9x 




.21 


1.75 


5.64 


15.10 


31.46 


43.59 


43 


9y 




.07 


1.20 


5.58 


15.65 


31.49 


44.57 


41 


lOx 




.11 


3.21 


9.72 


18.91 


31.76 


44.86 


45 


lOy 




.11 


.86 


3.09 


8.29 


14.84 


26.24 


49 


llx 






.11 


1.10 


3.82 


13.02 


24.35 


62 


iiy 






.27 


.60 


2.44 


9.96 


20.32 


53 


12x 






.03 


.40 


1.24 


4.12 


10.58 


55 


12y 






.07 


.37 


.86 


3.71 


8.48 


54 


13x 






.11 


.17 


.58 


1.55 


4.94 


56 


13y 








.14 


.38 


1.21 


3.61 



the median second grade pupil. Sentence No. 2, which received 
a score of 68.21 per cent in the second grade, is just 18.21 per 
cent too easy (68.21 —50.00 = 18.21) for the median child in this 
grade. Reference to Table XI 11/ which gives the P.E. values 
of each tenth of a per cent from 0.0 to 49.9 above or below 50 
per cent, indicates that 18.21 per cent difference is equal to .702 
P.E. We may therefore locate sentence No. 2 with reference 
to the second grade median as at —.702. Sentence No. 4, 
having a 69.57 per cent score, is just 19.57 P^r cent too easy 
(69.57 ~ 50.00 = 19.57) for the median second grade child, and ref- 
erence to Table XI 11 locates the sentence at a distance of .759 P.E. 
from the median. Since it is too easy for the median child, the 
sentence will be below the second grade median, or exactly — .759. 

^ Table XIII is taken directly from B. R. Buckingham's Spelling Ability 
(Table XLVII). It is a modification of the table given in E. L. Thorndike's 
Mental and Social Measurements (page 200). 



38 



Completion-Test Language Scales 



TABLE XIII 

P.E. Values Corresponding to Given Per Cents of the Normal Surface 
OP Frequency, Per Cents Being Taken From the Median 



% 


.0 


.1 


.2 


.3 


.4 


.5 


.6 


.7 


.8 


.9 





.000 


.004 


.007 


.011 


.015 


.019 


.022 


.026 


.030 


.033 


1 


.037 


.041 


.044 


.048 


.052 


.056 


.059 


.063 


.067 


.071 


2 


.074 


.078 


.082 


.085 


.089 


.093 


.097 


.100 


.104 


.108 


3 


.112 


.115 


.119 


.123 


.127 


.130 


.134 


.138 


.141 


.145 


4 


.149 


.153 


.156 


.160 


.164 


.168 


.172 


.175 


.179 


.183 


5 


.187 


.190 


.194 


.198 


.201 


.205 


.209 


.213 


.216 


.220 


6 


.224 


.228 


.231 


.235 


.239 


.243 


.246 


.250 


.254 


.258 


7 


.261 


.265 


.269 


.273 


.277 


.280 


.284 


.288 


.292 


.296 


8 


.299 


.303 


.307 


.311 


.315 


.318 


.322 


.326 


.330 


.334 


9 


.337 


.341 


.345 


.349 


.353 


.357 


.360 


.364 


.368 


.372 


10 


.376 


.380 


.383 


.387 


.391 


.395 


.399 


.403 


.407 


.410 


11 


.414 


.418 


.422 


.426 


.430 


.434 


.437 


.441 


.445 


.449 


12 


.453 


.457 


.461 


.464 


.468 


.472 


.476 


.480 


.484 


.489 


13 


.492 


.496 


.500 


.504 


.508 


.512 


.516 


.519 


.523 


.527 


14 


.531 


.535 


.539 


.543 


.547 


.551 


.555 


.559 


.563 


.567 


15 


.571 


.575 


.579 


.583 


.588 


.592 


.596 


.600 


.603 


.608 


16 


.612 


.616 


.620 


.624 


.628 


.632 


.636 


.640 


.644 


.648 


17 


.652 


.656 


.660 


.665 


.669 


.673 


.677 


.681 


.685 


.689 


18 


.693 


.698 


.702 


.706 


.710 


.714 


.719 


.723 


.727 


.731 


19 


.735 


.740 


.744 


.748 


.752 


.756 


.761 


.765 


.769 


.773 


20 


.778 


.782 


.786 


.790 


.795 


.799 


.803 


.807 


.812 


.816 


21 


.820 


.825 


.829 


.834 


.838 


.842 


.847 


.851 


.855 


.860 


22 


.864 


.869 


.873 


.878 


.882 


.886 


.891 


.895 


.900 


.904 


23 


.909 


.913 


.918 


.922 


.927 


.931 


.936 


.940 


.945 


.949 


24 


.954 


.958 


.963 


.968 


.972 


.977 


.982 


.986 


.991 


.996 


25 


1.000 


1.005 


1.009 


1.014 


1.019 


1.024 


1.028 


1.033 


1.038 


1.042 


26 


1.047 


1.052 


1.057 


1.062 


1.067 


1.071 


1.076 


1.081 


1.086 


1.091 


27 


1,096 


1.101 


1.105 


1.110 


1.115 


1.120 


1.125 


1.130 


1.135 


1.140 


28 


1.145 


1.150 


1.155 


1.160 


1.165 


1.170 


1.176 


1.181 


1.186 


1.191 


29 


1.196 


1.201 


1.206 


1.211 


1.217 


1.222 


1.227 


1.232 


1.238 


1.243 


30 


1.248 


1.253 


1.259 


1.264 


1.269 


1.275 


1.279 


1.286 


1.291 


1.296 


31 


1.302 


1.307 


1.313 


1.318 


1.324 


1.329 


1.335 


1.340 


1.346 


1.351 


32 


1.357 


1.363 


1.368 


1.374 


1.380 


1.386 


1.391 


1.397 


1.403 


1.409 


33 


1.415 


1.421 


1.427 


1.432 


1.438 


1.444 


1.450 


1.456 


1.462 


1.469 


34 


1.475 


1.481 


1.487 


1.493 


1.499 


1.506 


1.512 


1.518 


1.524 


1.531 


35 


1.537 


1.543 


1.549 


1.556 


1.563 


1.569 


1.576 


1.582 


1.589 


1.595 


36 


1.602 


1.609 


1.616 


1.622 


1.629 


1.636 


1.643 


1.649 


1.656 


1.663 


37 


1.670 


1.677 


1.685 


1.692 


1.699 


1.706 


1.713 


1.720 


1.728 


1.735 


38 


1.742 


1.749 


1.757 


1.765 


1.772 


1.780 


1.788 


1.795 


1.803 


1.811 


39 


1.819 


1.827 


1.835 


1.843 


1.851 


1.859 


1.867 


1.875 


1.884 


1.892 


40 


1.900 


1.909 


1.918 


1.926 


1.935 


1.944 


1.953 


1.962 


1.971 


1.979 


41 


1.988 


1.997 


2.007 


2.016 


2.026 


2.035 


2.044 


2.054 


2.064 


2.074 


42 


2.083 


2.093 


2.103 


2.114 


2.124 


2.134 


2.145 


2.155 


2.166 


2.177 


43 


2.188 


2.199 


2.211 


2.222 


2.234 


2.245 


2.257 


2 . 269 


2.281 


2.293 


44 


2.305 


2.318 


2.331 


2.344 


2.357 


2.370 


2.384 


2.397 


2.411 


2.425 


45 


2.439 


2.453 


2.468 


2.483 


2.498 


2.514 


2.530 


2.546 


2.562 


2.579 


46 


2.597 


2.614 


2.631 


2.648 


2.667 


2.686 


2.706 


2.726 


2.746 


2.767 


47 


2.789 


2.811 


2.834 


2.857 


2.881 


2.905 


2.932 


2.958 


2.986 


3.015 


48 


3.044 


3.077 


3.111 


3.146 


3.182 


3.219 


3.258 


3.300 


3.346 


3.395 


49 


3.460 


3.506 


3.571 


3.643 


3.725 


3.820 


3.938 


4.083 


4.275 


4.600 


% 


.0 


.1 


.2 


.3 


.4 


.5 


.6 


.7 


.8 


.9 



Calculation of the Difficulty of Test Sentences 



39 



Table XIV shows the differences between 50 per cent (or the 
grade median) and the percentages given in Table XII. Table 
XV shows the P.E. equivalents of these differences shown in 
Table XIV, or the location of each sentence of Scale A with 
reference to the median of each elementary grade. 

TABLE XIV 

Difference Between Fifty Per Cent and Per Cent op Perfect Score 
Made By Each Elementary Grade for Each Sentence of Lan- 
guage Scale A 



Sentence 


Grade 


Grade 


Grade 


Grade 


Grade 


Grade 


Grade 




No. 


II 


III 


IV 


V 


VI 


VII 


VIII 


2 


2x 


18.21 


40.36 


44.32 


45.68 


44.64 


47.01 


46.92 


4 


2y 


19.57 


42.55 


46.14 


48.19 


48.52 


49.07 


48.74 


7 


3x 


-28.18 


5.46 


26.79 


38.52 


44.57 


48.01 


48.14 


11 


3y 


-28.45 


6.09 


27.72 


39.71 


44.46 


46.36 


47.79 


22 


4x 


-43.63 


-25.15 


6.63 


28.99 


38.31 


46.05 


47.44 


29 


4y 


-42.71 


-16.56 


11.07 


31.95 


41.13 


44.99 


47.76 


23 


5x 


-45.87 


-26.02 


-5.13 


12.41 


23.93 


32.59 


38.58 


24 


5y 


-45.28 


-30.72 


-13.15 


8.89 


23.28 


32.69 


39.88 


27 


6x 


-47.61 


-33.05 


-16.95 


- 5.91 


3.03 


12.95 


18.08 


31 


6y 


-48.54 


-36.64 


-15.85 


- 6.30 


9.18 


16.96 


21.83 


28 


7x 


-48.59 


-41.02 


-27.34 


-13.83 


0.79 


11.47 


17.45 


30 


7y 


-49.41 


-41.82 


-26.89 


-13.33 


0.03 


10.95 


19.62 


37 


8x 


-49.85 


-47.88 


-38.14 


-28.37 


-14.68 


0.27 


5.12 


34 


8y 


-49.71 


-45.30 


-35.27 


-25.02 


- 9.39 


2.37 


12.05 


36 


9x 




-49.79 


-48.25 


-44.36 


-34.90 


-18.54 


- 6.41 


43 


9y 




-49.93 


-48.80 


-44.42 


-34.35 


-18.51 


- 5.43 


41 


lOx 




-49.89 


-46.79 


-40.28 


-31.09 


-18.24 


- 5.14 


45 


lOy 




-49.89 


-49.14 


-46.91 


-41.71 


-35.16 


-23.76 


49 


llx 






-49.89 


-48.90 


-46.18 


-36.98 


-25.65 


52 


iiy 






-49.73 


-49.40 


-47.56 


-40.04 


-29.68 


53 


12x 






-49.97 


-49.60 


-48.76 


-45.88 


-39.42 


55 


12y 






-49.93 


-49.63 


-49.14 


-46.29 


-41.52 


54 


13x 






-49.89 


-49.83 


-49.42 


-48.45 


-45.06 


56 


13y 








-49.86 


-49.62 


-48.79 


-46.39 



The figures shown in Table XV form for each elementary- 
grade the final measure of the difficulty of any given sentence for 
that grade. If it were not desirable to show the difffculty of 
each sentence for all grades together, we might use the values of 
Table XV without making any further changes in them. In- 
deed, if any person desires to know the difficulty of any sentence 
in Scale A for the fifth grade or for any other elementary grade, 
Table XV gives the necessary data. 

The measurement of the difficulty of these sentences in the 



40 



Completion-Test Language Scales 



TABLE XV 

P.E. Equivalent op Difference Between 50 Per Cent and Per Cent 
OF Perfect Score Made by Each Elementary Grade for Each 
Sentence of Language Scale A 



Sentence 


Grade 


Grade 


Grade 


Grade 


Grade 


Grade 


Grade 


No. 


II 


III 


IV 


V 


VI 


VII 


VIII 


2 


2x 


-.702 


-1.931 


-2.347 


-2.543 


-2.389 


-2.791 


-2.769 


4 


2y 


-.759 


-2.140 


-2.621 


-3.107 


-3.227 


-3.489 


-3.318 


7 


3x 


1.154 


- .203 


-1.086 


-1.782 


-2.380 


-3.047 


-3.091 


11 


3y 


1.168 


- .228 


-1.131 


-1.876 


-2.365 


-2.659 


-2.983 


22 


4x 


2.261 


1.007 


- .247 


-1.196 


-1.766 


-2.605 


-2.891 


29 


4y 


2.156 


.634 


- .417 


-1.354 


-2.000 


-2.438 


-2.975 


23 


5x 


2.574 


1.048 


.191 


- .468 


- .951 


-1.391 


-1.786 


24 


5y 


2.480 


1.287 


.498 


- .334 


- .921 


-1.396 


-1.890 


27 


6x 


2.935 


1.418 


.650 


.220 


- .113 


- .491 


- .697 


31 


6y 


3.235 


1.645 


.605 


.235 


- .344 


- .650 


- .857 


28 


7x 


3.254 


1.990 


1.112 


.524 


- .030 


- .433 


- .671 


30 


7y 


3.734 


2.066 


1.091 


.505 


- .001 


- .412 


- .762 


37 


8x 


4.437 


3.009 


1.752 


1.164 


.558 


- .010 


- .191 


- 34 


8y 


4.102 


2.483 


1.554 


1.001 


.353 


- .088 


- .455 


36 


9x 




4.256 


3.129 


2.352 


1.531 


.716 


.239 


43 


9y 




4.720 


3.346 


2.360 


1.495 


.715 


.202 


41 


lOx 




4.568 


2.744 


1.924 


1.307 


.704 


.192 


45 


lOy 




4.568 


3.532 


2.769 


2.055 


1.547 


.943 


49 


llx 






4.567 


3.395 


2.628 


1.669 


1.031 


52 


iiy 






4.151 


3.725 


2.921 


1.904 


1.231 


53 


12x 






4.880 


3.938 


3.328 


2.576 


1.853 


55 


12y 






4.720 


3.982 


3.532 


2.646 


2.037 


54 


13x 






4.567 


4.372 


3.744 


3.200 


2.447 


56 


13y 








4.475 


3.967 


3.341 


2.665 



higher grades is made in exactly the same manner as it was made 
in the elementary grades: the score on each sentence is turned 
into percentages of the perfect score, the differences between these 
percentages and 50 per cent being then turned into P.E. dififer- 
ences by means of Table XIII. This assumes, of course, that 
ability to complete sentences is distributed according to the 
normal surface of frequency in each higher grade. The score 
and the P.E. distances from the medians are given in Table XVI 
for the eighth grade and high school classes in those school sys- 
tems where the writer was able to test both the elementary and 
high school classes. The same facts are shown for the group of 
graduate students at Teachers College. 



Calculation of the Difficulty of Test Sentences 



41 



TABLE XVI 

Score and P.E. Equivalents for Each Sentence op Language Scale A 
IN the Higher Grades (Complete System Group) 



Sentence 
No. 


Grade 
VIII 


Grade 
IX 


Grade 
X 


Grade 
XI 


Grade 
XII 


College 
Graduates 


8 

CO 


P.E. 




P.E. 




02 


P.E. 


£ 


IB 


P.E. 





P.E. 


£ 



CO 


P.E. 


2 
4 
7 
11 
. 22 
29 
23 
24 
27 
31 
28 
30 
37 
34 
36 
43 
41 
45 
49 
52 
53 
55 
54 
56 


421 

431 

435 

430 

426 

433 

373 

390 

285 

327 

296 

304 

244 

239 

161 

165 

144 

102 

76 

44 

19 

23 

11 

11 


—2.470 
—2.908 
—3.190 
-2.852 
—2.663 
—2.032 
—1.499 
—1.760 

— .550 

— .953 

— .651 

— .726 
—1.95 
—1.52 
+ .515 
+ .479 
+ .670 
+ 1.092 
+ 1.403 
+1.904 
+2.546 
+2.411 
+2.908 
+2.908 


541 
534 
531 
526 
538 
538 
496 
483 
404 
443 
390 
409 
358 
346 
289 
321 
275 
210 
188 
143 
92 
62 
44 
26 


—3.495 
—2.986 
—2.846 
—2.652 
—3 . 235 
—3.235 
—1.974 
—1.769 

— .954 
—1.309 

— .839 

— .996 

— .595 

— .507 

— .109 

— .330 

— .014 
+ .435 
+ .595 
+ .945 
+1.424 
+ 1.777 
+2.078 
+2.474 


334 
340 
340 
337 
333 
336 
308 
314 
291 
288 
269 
266 
251 
269 
209 
222 
218 
165 
160 
157 
110 
97 
61 
29 


—2.953 
—3.735 
—3.735 
—3.235 
—2 . 874 
—3.125 
—1.905 
—2.065 
—1.543 
—1.487 
—1.178 
—1.134 

— .927 
—1 . 179 

— .418 

— .567 

— .521 
+ .065 
+ .120 
+ .153 
+ .687 
+ .849 
+1.366 
+2.037 


271 
270 
261 
259 
272 
269 
242 
261 
244 
252 
223 
223 
187 
220 
188 
201 
168 
167 
131 
140 
106 
94 
71 
45 


—3.983 
—3.614 
—2.586 
—2.471 
1 

—3'. 395 
—1.817 
—2.586 
—1.875 
—2.150 
—1.357 
—1 . 357 

— .725 
—1.295 

— .741 

— .949 

— .444 

— .429 
+ .068 

— .055 
+ .415 
+ .590 
+ .949 
+1.441 


206 
202 
206 
205 
205 
206 
185 
192 
180 
191 
167 
177 
164 
179 
149 
149 
159 
126 
129 
119 
88 
78 
40 
41 


? 
—3.064 

? 
—3.832 
—3.832 

? 

— 1'.885 
—2.211 
—1.698 
—2.157 
—1.305 
—1.597 
—1.227 
—1.663 

— .879 

— .879 
—1 . 104 

— .420 

— .477 

— .291 
+ .272 
+ .459 
+1.278 
+1.253 


220 
228 
226 
227 
228 
228 
224 
223 
212 
210 
186 
208 
193 
205 
192 
215 
190 
189 
187 
204 
145 
149 
136 
105 


—2.684 

? 
—3.519 
—3.891 

? 

7 
—3.125 
—2.989 
—2.186 
—2.093 
—1.334 
—2.010 
—1.515 
—1.893 
—1.488 
—2.344 
—1.434 
—1.409 
—1.358 
—1.857 

— .516 

— .585 

— 3.62 
+ .147 


No of 
Pupils . 


221 




273 




171 




136 




103 




114 




Perfect 
Score . 


442 




546 




342 




272 




206 




228 





4, Measurement of the Distances Between Grades 

There are a number of ways in which the P.E. distances be- 
tween consecutive grades can be measured. Three methods 
have been used in this study and the average of the three has 
been taken as the most probably true measure of the distance in 
each case. 

We have assumed that the ability to complete sentences is 
distributed in any given grade in accordance with the normal 
surface of frequency. The assumption was also made, although 
it was not clearly stated, that each sentence to be completed is a 
test of ability to complete sentences, and that ability to complete 
individual sentences is distributed "normally." The difference 
between two consecutive grades may therefore be measured by 
the difference in the positions with reference to the two grade 
medians held by any given sentence. For example, sentence 



42 



Completion-Test Language Scales 



No. 2 was, according to Table XV, .702 P.E. below the second 
grade median and 1.931 P.E. below the third grade median, which 
makes a difference of 1.229 P-E. between the medians of the 
second and third grades. This method of determining the 
differences gives us a large number of direct measurements. 
Table XVII gives these sentence measurements of the intervals 
between the consecutive elementary grades. 

TABLE XVII 

P.E. Intekvals Shown Between Consecutive Elementary Grades by 
Each Sentence op Language Scale A 



Sentence 


Interval 


Interval 


Interval 


Interval 


Interval 


Interval 


No. 


II-III 


III-IV 


IV-V 


V-VI 


VI-VII 


VII-VIII 


2 2x 


1.229 


.416 


.196 


-.154 


.402 


-.022 


4 2y 


1.381 


.481 


.486 


.120 


.262 


-.171 


7 3x 


1.357 


.883 


.696 


.598 


.667 


.044 


11 3y 


1.396 


.903 


.745 


.489 


.294 


.324 


22 4x 


1.254 


1.254 


.949 


.570 


.839 


.286 


29 4y 


1.522 


1.051 


.937 


.646 


.438 


.537 


23 5x 


1.526 


.857 


.659 


.483 


.440 


.395 


24 5y 


1.193 


.789 


.832 


.587 


.475 


.494 


27 6x 


1.517 


.768 


.430 


.333 


.378 


.206 


31 6y 


1.590 


1.040 


.370 


.579 


.306 


.207 


28 7x 


1.264 


.878 


.588 


.554 


.403 


.238 


30 7y 


1.668 


.975 


.586 


.506 


.411 


.350 


37 8x 


1.428 


1.257 


.588 


.606 


.568 


.181 


34 By 


1.619 


.929 


.553 


.648 


.441 


.367 


36 9x 




1.127 


.777 


.821 


.815 


.477 


43 9y 




1.374 


.986 


.865 


.780 


.513 


41 lOx 




1.824 


.820 


.617 


.603 


.512 


45 lOy 




1.036 


.763 


.714 


.508 


.604 


49 llx 






1.172 


.767 


.959 


.638 


52 lly 






.426 


.804 


1.017 


.673 


53 12x 






.942 + 


.610 


.752 


.723 


55 12y 






.738 + 


.450 


.886 


.609 


54 13x 






.195 


.628 


.544 


.753 


56 13y 








.508 


.626 


.676 


Average. . . 


1.425 


.991 


.671 


.556 


.576 


.401 



A general tendency will be noticed in Table XVII for the 
large differences between grades to appear in the harder sentences. 
I have grouped the measurements of each interval, putting in 
one group those measurements of the interval shown in Table 
XVII which were obtained from values lower than —1.5 P.E. 
in Table XV, in a second group those obtained from values 



Calculation of the Difficulty of Test Sentences 



43 



between —1.5 and 1.5 P.E., and in a third group those measure- 
ments obtained from positive values larger than 1.5 P.E. The 
average of each group of measurements for each interval is 
given below in Table XVIII. 

TABLE XVIII 

Averages of Groups of Determinations of Inter-Grade Intervals as 
Measured by Sentences of Language Scale A 



Group 



Interval 
II-III 



Interval 
III-IV 



Interval 
IV-V 



Interval 
V-VI 



Interval 
VI-VII 



Interval 
VII-VIII 



Below —1.5 
-1.5 to 1.5 
Above 1.5 



1.305 


.448 


.531 


.378 


.484 


1.376 


.929 


.669 


.537 


.511 


1.558 


1.160 


.724 


.678 


.756 



.236 
.339 
.668 



Table XVIII throws some very interesting light upon the 
question of how two grades differ in ability. Evidently one 
grade is better than the grade below both in the difficult and the 
easy tests, but the large differences are in the hard tests. An 
eighth grade child differs from a seventh grade child more dis- 
tinctly in doing difficult tasks than in doing tasks that are 
moderately easy for both. At any rate, it appears that the 
child in the higher grade shows his superiority in doing harder 
tests rather than in doing the easy tests. 

It hardly seems just to allow the intervals between grades to 
be influenced equally by sentences near the medians of the two 
grades concerned and by other sentences at the extreme ranges 
of the distributions. The sentences near the medians are more 
reliable measures and should probably be weighted, while those 
sentences which are more than 3 or 4 P.E. from the interval 
should possibly not be allowed to influence the measure of the 
interval at all, because at that extreme range caprice and accident 
have undue influence. It also seems unfair, in view of the facts 
shown in Table XVIII, to allow the easy sentences to have the 
same amount of influence as the more difficult in determining 
the intervals between grades. The plan that has been followed 
here has been to allow equal weight to all measures of the interval 
by sentences not more than 2 P.E. below the lower grade of the 
pair nor more than 4 P.E. above the higher grade of the pair 



44 



Completion-Test Language Scales 



whose distance from each other is being measured. The average 
of the measurements by sentences in Table XVII, which lie 
within this range, are given below. 



Grade Interval .... II-III 
P.E. Interval 1.408 



III-IV 
.965 



IV-V 

.705 



V-VI 
.620 



VI-VII 
.606 



VII-VIII 

.479 



The intervals between the higher grades derived from the 
sentence locations given in Table XVI are shown in Table XIX, 
with the average of the determinations from sentences within 
the range —2 P.E. to +4 P.E. 

TABLE XIX 

P. E. Intekvals Shown Between Consecutive Higher Grades by Each 
Sentence of Language Scale A. (Complete System Group) 



Sentence 


Interval ^ 


Interval 


Interval 


Interval 


Interval 


No. 


VIII-IX 


IX-X 


X-XI 


XI-XII 


XII-C.G. 


2 


1.025 


-.542 


1.030 






4 


.078 


.749 


- .121 


-.550 




7 


-.344 


.889 


-1.149 






11 


-.200 


.583 


- .764 


1.361 


.059 


22 


.572 


-.993 








29 


1.203 


-.110 


.270 






23 


.475 


-.069 


- .088 


.068 


1.240 


24 


.009 


.296 


.521 


-.375 


.778 


27 


.404 


.589 


.332 


-.177 


.488 


31 


.356 


.178 


.663 


.007 


-.064 


28 


.188 


.339 


.179 


-.052 


.029 


30 


.270 


.138 


.223 


.240 


.413 


37 


.400 


.332 


- .202 


.502 


.288 


34 


.355 


.672 


.116 


.368 


.230 


36 


.624 


.309 


.323 


.138 


.609 


43 


.809 


.237 


.382 


-.070 


1.465 


41 


.684 


.507 


- .077 


.660 


.330 


45 


.657 


.370 


.494 


-.009 


.989 


49 


.808 


.475 


.052 


.545 


.881 


52 


.959 


.792 


.208 


.236 


1.566 


53 


1.122 


.737 


.272 


.143 


.788 


55 


.634 


.928 


.259 


.131 


1.044 


54 


.830 


.712 


.417 


-.329 


1.640 


56 


.434 


.437 


.596 


.188 


1.106 


Weighted 












Average 


.556 


.484 


.265 


.192 


.813 



I In each of the methods used to determine the intervals between consecutive grades, the 
difference between the eighth grade and the first year high school grade has been based upon 
the difference found in those school systems where both elementary and high school classes 
were tested. 

Table XIX has the disadvantage of being based upon the 
small number of pupils tested in those school systems where both 



Calculation of the Difficulty of Test Sentences 



45 



elementary and high school grades were measured. Six sentences 
included in this group were also included in some tests given in 
three large city high schools, so that it is possible to get from 
them a measure of the differences between high school grades 
based upon a larger number of pupils, although upon a smaller 
number of sentences. 

Table XX gives the score and P.E, equivalents for these six 
sentences in the high school grades. 

TABLE XX 
Score and P.E. Equivalents for Six Sentences in the Higher Grades 





Grade IX 


Grade X 


Grade XI 


Grade XII 


Col. Grads. 


Sentence 


















No. 


o 

02 


P.E. 


o 
w 


P.E. 


o 
o 


P.E. 


O 
O 
CO 


P.E. 


o 
o 

m 


P.E. 


37 


692 


-.548 


560 


-.763 


630 


-.653 


544 


- .805 


193 


-1.515 


36 


575 


-.132 


542 


-.669 


630 


-.653 


587 


-1.059 


192 


-1.488 


45 


403 


.471 


388 


.065 


491 


-.083 


468 


- .406 


189 


-1.409 


49 


335 


.727 


378 


.111 


489 


-.075 


477 


- .451 


187 


-1.358 


55 


124 


1.777 


190 


1.065 


293 


.728 


320 


.316 


149 


- .585 


54 


53 


2.447 


101 


1.702 


142 


1.531 


157 


1.227 


136 


- .362 


No. tested. . . . 


537 




402 




470 




385 




114 





The averages of the six determinations from Table XX of the 
intervals between grades, I have calculated to be as shown in the 
second line below. 

IX-X X-XI XI-XII XII-C.G. 

Language Scale A 484 .265 .192 .813 

Six Sentences 538 .119 .329 .923 

Average to use 511 .192 .260 .868 

The third line shows the intervals which will be used as probably 
the most accurate determinations from sentences. 

A second method of determining the intervals between grade 
medians makes use of the quartile as a measure of the P.E. If 
Scale A were perfect and if the surfaces of distribution in Figs. 
8 to 14 were perfectly normal, the quartile, which is half of the 
range of the middle 50 per cent, would have been exactly the 
same as the P.E. Since we are assuming in the other determina- 
tions that completion-test surfaces of distribution are approxi- 



46 



Completion-Test Language Scales 



mately normal, no great error will result from doing so in this 
case. I have therefore averaged the quartiles of each two con- 
secutive grades and used this average as a diviser of the crude 
score interval between the grade medians. Table XXI shows 
the result upon the data furnished by Table I. 



TABLE XXI 

Determination of the Quartile Intervals Between Elementary 

Grades 





Grade 
II 


Grade 
III 


Grade 
IV 


Grade 
V 


Grade 
VI 


Grade 
VII 


Grade 
VIII 


Median Score . . . 
Quartile 


4.5912 
2.0848 


8.9864 
3.4127 


14.3287 
4.1567 


18.3888 
3.6140 


21.9175 
3.6098 


25.2719 
3.7496 


28.0598 
4.0412 


Score Interval 

Average Quartile .... 


4.3952 

2.7487 


5.3423 

3.7847 


4.0601 

3.8858 


3.5287 
3.6119 


3.3544 
3.6797 


2.7879 
3.8954 




Quartile Interval .... 


1.5990 


1.4115 


1 .0450 


.9769 


.9116 


.7157 





Table XXII furnishes the same information regarding the 
quartile intervals between the higher grades, from the data 
given in Table III. 



TABLE XXII 

Determination of the Quartile Intervals Between Higher Grades 

(Complete System Group) 





Grade 
VIII 


Grade 
IX 


Grade 
X 


Grade 
XI 


Grade 
XII 


College 
Gradu- 
ates 


Median Score 

Quartile 


27.8611 
3.6882 


30.1470 
4.2317 


33.6818 
3.8992 


35.7272 
3.3718 


37.1666 
3.8437 


42.8125 
2.8660 


Score Interval 


2.2859 
3.9599 


3.5348 
4.0654 


2.0454 
3.6355 


1.4394 
3.6077 


5.6459 
3.3548 




Average Quartile 




Quartile Interval 


.5772 


.8695 


.5626 


3989 


1.6829 





























Calculation of the Difficulty of Test Sentences 47 

The third measurement of the differences between successive 
grades is also based upon the distribution of scores in Language 
Scale A. It will be observed in Table I that many second grade 
pupils received scores greater than the median score for the 
third grade, and that many third grade pupils received lower 
scores than the median second grade score. Between the third 
grade median, which is 8.9864, and the second grade median, 
which is 4.5912, there are (if we assume that the scores of the 
children recorded as making a given score are spread evenly 
over that step) 531.96 of the 131 8 individuals in the second grade 
distribution and 545.58 of the 1437 individuals in the third grade 
distribution. In terms of percentages, 37.96 per cent of the 
third grade distribution and 40.36 per cent of the second grade 
distribution lie between the medians of these two grades. Each 
of these percentages is a percentage from the median of the 
distribution and may therefore be turned at once into a P.E. 
value by means of Table XIII. This transmutation reveals 
a difference between the medians of the second and third grades 
of 1. 931 P.E. when measured by the second grade distribution, 
and 1.739 when measured by the third grade distribution. 

It is also possible by this method to obtain certain indirect 
measures of the same distances. 47.66 per cent of the fourth 
grade distribution, for example, lies between the fourth grade 
median and the second grade median, so we may say (from 
Table XIII) that in so far as it is measured directly by the 
fourth grade distribution the second grade median is 2.948 P. E. 
below the median of the fourth grade. In the same way, 31.55 
per cent of the fourth grade distribution lies between the median 
for that grade and the median for the third grade, which makes 
a P.E. difference of 1.332 between the two grades. From the 
median of the fourth grade distribution, then, we have found it 
to be 2.948 P.E. to the second and 1.332 P.E. to the third grade 
median, and by subtraction this gives us a difference between the 
second and third grade medians of 1.616 P.E. 

It would be possible, of course, to derive indirect measures 
of each interval from any distribution of scores which covers the 
interval, but it would be unfair to allow these indirect measure- 
ments, especially those which are very near the extreme ranges 
of a distribution, to have the same influence as the direct measure- 
ments. Since the intervals have already been determined by 



48 



Completion-Test Language Scales 



two other methods, it seemed best to give full weight here to 
direct determinations by this method and one-half weight to the 
indirect determinations obtained from the distribution next above 
the pair furnishing direct determinations and one-half weight 
to the indirect determination obtained from the distribution 
next below the direct pair. 

Table XXIII gives for each elementary grade distribution 
the percentages of the distribution lying between its median 
and the medians of the two grades lower and of the two grades 
higher, and the P.E. equivalents of these percentages as taken 
from Table XIII. 

TABLE XXIII 

Percentages of Each Elementary Grade Distribution Lying Between 
Its Median and the Medians op Neighboring Grades, with P.E. 
Equivalents 





Percentages and Equivalents of Percentages of Distribution of 


To Median 
of Grade 








Grade 
II 


Grade 
III 


Grade 
IV 


Grade 
V 


Grade 
VI 


Grade 
VII 


Grade 
VIII 


Grade 
IX 


II 




37.96% 
1.739 


47.66% 
2.948 












III 


40.36% 
1.931 




31 . 55% 
1.332 


46.70% 
2.726 










IV 


48.30% 
3.146 


30.45% 
1.272 




28.07% 
1.148 


40.82% 
1.973 








v 




43.43% 
2.237 


23.94% 
.951 




23.62% 
.937 


38.91% 
1.812 






VI 






39.33% 
1.845 


24.35% 
.970 




23.13% 
. .910 


36.28% 
1.621 




VII 








40.15% 
1.914 


24.60% 
.982 




19.14% 
.742 


30.16% 
1.257 


VIII 










37.82% 
1.729 


18.78% 
.726 




13.04% 
.494 



As indicated above, the direct determinations are given twice 
as much weight in this study as the indirect values, and the only 
indirect values used are those from the distributions. immedi- 
ately above and below the grades concerned. Table XXIV 
shows the values used. 



Calculation of the Difficulty of Test Sentences 
TABLE XXIV 



49 



Deteeminations of the Inter-Grade Intervals Obtained from Over- 
lapping OP Distributions of Scores on Language Scale A 



Determination 


II-III 


III-IV 


IV-V 


V-VI 


VI-VII 


VII-VIII 


Lower Indirect . . 
Lower Direct . . . 

Upper Direct . . . 

Upper Indirect . . 


1.931 
1.931 
1.739 
1.739 
1.616 


1.215 
1.272 
1.272 
1.332 
1.332 
1.578 


.965 

.951 

.951 

1.148 

1.148 

1.036 


.894 
.970 
.970 
.937 
.937 
.902 


.944 
.982 
.982 
.910 
.910 
.879 


.747 
.726 
.726 
.742 
.742 
.763 


Average 


1.7912 


1.3335 


1.0331 


.9350 


.9345 


.7410 



Table XXV gives data similar to Table XXIII but with refer- 
ence to the higher grades in those schools where the entire school 
system was tested. The distributions of scores in Language 
Scale A upon which Table XXV is based will be found in Table 
III. 

TABLE XXV 

Percentages op Each Higher Grade Distribution Lying Between Its 
Median and the Medians op Neighboring Grades, with P.E. 
Equivalents 









Distribution of 






To Median 
of Grade 














Grade 
VII 


Grade 
VIII 


Grade 
IX 


Grade 
X 


Grade 
XI 


Grade 
XII 


Grade 
C.G 


VIII 


17.12% 
.657 




14.44% 
.549 


36.03% 
1.604 








IX 


29.13% 
1.203 


16.29% 
.624 




24.65% 
.984 


32.65% 
1.394 






X 




35.49% 
1.568 


20.39% 
.795 




16.04% 
.614 


21.75% 
.853 




XI 






31.32% 
1.319 


10.36% 
.389 




9.13% 
.342 


40.43% 
1.938 


XII 








16.77% 
.643 


7.23% 
.270 




35.38% 
1.561 


C.G. 










41.63% 
2.047 


33.92% 
1.470 





The averages of the weighted direct values and the unweighted 
indirect values obtained from Table XXV, as illustrated in Table 
XXIV, are as follows: 



50 



Completion-Test Language Scales 



Interval VIII-IX IX-X X-XI XI-XII XII-C.G. 

Average 5853 .8803 .5068 .3091 1 .5678 

Half of the sentences in Language Scale A were included in a 
test given in two high schools where the elementary grades had 
not been tested. The sentences included in this high school test 
were selected, one sentence from each grade-pair in Scale A, so 
that the entire test had practically the same difficulty but was 
just half as long as Language Scale A. By going through the 
records and finding what score each student in the higher grades 
would have made if tested on these twelve sentences only, I was 
able to get a distribution of scores in each of these higher grades 
which had the advantage of larger numbers of pupils, although 
there were fewer sentences. Table XXVI shows the total dis- 

TABLE XXVI 

DiSTEIBUTION OF ScORES MaDE IN HiGH SCHOOL HaLF TeST 



Score 


Grade 
IX 


Grade 
X 


Grade 
XI 


Grade 
XII 


Col. Grads. 


24 


1 

1 

10 

9 

15 

27 

29 

24 

24 

32 

32 

24 

21 

10 

6 

5 

2 

1 


3 

6 

8 

9 
11 
24 
17 
22 
30 
25 
17 
15 
10 

8 

3 

2 

2 
........ 


2 

1 

16 

14 

34 

42 

53 

31 

34 

39 

21 

17 

15 

12 

4 

2 

2 

1 


5 

6 

12 

19 

24 

28 

33 

27 

19 

31 

12 

11 

6 

1 

2 

1 


13 


23 


17 


22 


23 


21 


13 


20 


15 


19 


12 


18 


11 


17 

16 

15 


6 
2 


14 




13 

12 


1 


11 

10 


1 


9 




8 




7 






6 






5 








4 . . . . 












3 












2 












1 





































No. tested 


273 


213 


340 


237 


114 


Median Score 


15.14 


16.78 


17.74 


18.26 


21.69 







Calculation of the Difficulty of Test Sentences 



51 



tribution of scores made in this high school half-test by the pupils 
in Grade IX and above, whether they took it in the short form 
or as a part of Scale A. 

From this table I have worked out the distances between grade 
medians in exactly the same way as they were derived above, 
with the following results: 



Interval IX-X 

Average 6968 



X-XI 

.3828 



XI-XII 

.2458 



XII-C.G. 

1.8054 



As being probably the truest value for the intervals as deter- 
mined by this method, I have taken the average of the determina- 
tion by the small number of pupils with Scale A and the deter- 
mination by the larger number of pupils with half of Scale A. 



Interval 


VIII-IX 


IX-X 


X-XI 


XI-XII 


XII-C.G 


From Scale A 


.5853 


.8803 


.5068 


.3091 


1.5678 


From half Scale A . 




.6968 


.3828 


.2458 


1 .8054 


Av. Determination 






















of Distributions . . 


.5853 


.7885 


.4448 


.2774 


1.6866 



Values for the intervals between grade medians having now 
been worked out by three different methods, it is interesting to 
note that although the three determinations differ somewhat, 
their general characteristics are the same. It would be difficult 
to determine which method furnishes the best results. I have 
simply taken the average of the three results for each interval as 
the one to be used in this study. The results of each method 
and the average result are given in Table XXVII. 



TABLE XXVII 
Three Determinations of the Interval Between Successive Grades 



Method 


Interval Between Grades 






10 
1 


CD 
1 
10 


1 

CD 


00 


1 
00 




i-H 


T— 1 


I— 1 

1 

rH 
7— ( 


|0 
2d 


Sentence 

Distribution . . . 
Quartile 


1.408 
1.791 
1.599 


.965 
1.333 
1.411 


.705 
1.033 
1.045 


.620 
.935 
.977 


.606 
.934 
.912 


.479 
.741 
.716 


.556 
.585 
.577 


.511 

.788 
.869 


.192 
.445 
.563 


.260 

.277 
.399 


.868 
1.687 
1.683 


Average used as 
the final meas- 
ure 


1.599 


1.237 


.928 


.844 


.817 


.645 


.573 


.723 


.400 


.312 


1.412 







52 Completion-Test Language Scales 

5. Selection of a Zero- Point for Completion-Test Ability 

Zero-points are absolute on some scales and arbitrary on others. 
It would be very hard to select a sentence so easy that to be 
unable to complete it would signify that one had absolutely no 
"language ability, " so it will be necessary to choose an arbitrary 
zero-point for these tests if they are to be called "Language 
Scales. " It will still be possible, however, to locate a zero-point 
which will represent absolute inability to complete any printed 
sentence as difficult as the easiest one used in the tests included 
in this study. 

Reference to Table I shows that 255 of the 13 18 children in 
the second grade made a score of o in Scale A, which means that 
they received no score at all. Between these children and the 
median of the second grade, however, there were 404 children, 
which is 30.65 per cent of all in the second grade. Reference to 
Table XIII shows that a difference of 30.65 per cent from the 
median of a normal distribution means a distance of 1.283 P.E. 
If this were our only evidence, therefore, we might locate our 
arbitrary zero-point at 1.283 P-E. below the median of the second 
grade. 

Table I also shows that 19 of the 1437 pupils in the third grade 
made a score of zero, while 48.68 per cent scored above zero but 
below the median of their grade. This would locate the zero- 
point in Scale A at 3.291 P.E. below the third grade median. We 
have already determined (Table XXVII) that the third grade 
median is 1.599 P.E. above the second grade median. The 
zero-point in Scale A is therefore located by the third grade 
distribution at 1.692 (3.291 — 1.599 = 1.692) P.E. below the 
second grade median. 

The median score of the second grade on Language Scale A is 
shown by Table I to be 4.5912, and the quartile 2.0848. Assum- 
ing that the quartile is equal to the P.E., as it is in a perfectly 
normal surface of frequency, we find by dividing the score by the 
quartile that the second grade median is 2.2022 P.E. above zero. 

The median score of the third grade is shown by Table I to be 
8.9864. Table XXI shows the average of the quartiles of grades 
II and III to be 2.7487. Dividing the score by this average of 
the quartiles places the third grade median at 3.2693 P.E. above 
zero. From this determination, then, zero would be 1.670 



Calculation of the Difficulty of Test Sentences 53 

(3.269—1.599 = 1.670) P.E. below the second grade median. 
This makes the fourth determination of the distance from zero 
to the second grade median. The four determinations are as 
follows : 

From the second grade distribution 1 . 283 

From the third grade distribution 1 . 692 

From the second grade score 2 . 202 

From the third grade score 1 .670 

Average 1 .712 

It would be very convenient in any scale for ability of any sort 
to have at least one test located exactly one unit above the zero- 
point. The easiest sentence in Scale A is shown by Table XV 
to be sentence No. 4, "We are going _school." 

After accepting tentatively the determination just made that 
the second grade median is 1.712 P.E. above the zero-point, the 
location above zero of sentence No. 4 was worked out according 
to the scheme to be described below. It was found that, under 
these conditions, this sentence No. 4 had a value of 1.018 above 
zero. This was so near i.ooo that it was decided to employ 
such a value for the distance between zero and the second 
grade median as would place sentence No. 4 exactly at i P.E. 
above zero. 1.687 P-E. was found to be such a value. This 
is only .025 P.E. smaller than the average of the four deter- 
minations made above and is probably just as near the true 
distance. 

For the purposes of this study, then, zero will be defined arbi- 
trarily as I P.E. below sentence No. 4, or as 1.687 P-E. below the 
median of the second grade distribution shown in Table I."^ 

Having located our zero-point at 1.687 P.E. below the second 
grade median, and having previously determined the distances 
between the medians of each consecutive grade, it is now an easy 

^ It must be borne in mind that this is not a zero-point for language ability 
or even for completion-test ability, but merely the zero-point for ability to 
complete the printed sentences used in this study. The zero-point for ability 
to complete a spoken sentence would probably be found several units below 
the zero-point used in this study. The absolute zero-point for ability to 
complete the easiest possible incomplete idea or. representation of an object 
would probably be found still further down on an absolute scale, below even 
the zero-point for ability to complete a spoken sentence. If scales are ever 
constructed for these simpler forms of completion test, we may expect the zero- 
point established in this study to be located several units above the zero-point 
for these simpler tests. 



54 Completion-Test Language Scales 

matter to calculate the distance of each grade above zero. 
These distances are shown in Table XXVIII. 

TABLE XXVIII 
Distances Above Zeko op the Medians op Each School Grade. 1 =P.E. 



Grade 


Above Zero 


Below Next Grade 


II 


1.687 


1.599 


III 


3.286 


1.237 


IV 


4.523 


.928 


V 


5.451 


.844 


VI 


6.295 


.817 


VII 


7.112 


.645 


VIII 


7.757 


.573 


IX 


8.330 


.723 


X 


9.053 


.400 


XI 


9.453 


.312 


XII 


9.765 


1.412 


C.G. 


11.177 





Fig. 17 (page 55) represents the relations of the grade medians 
to each other, to the zero-point, and to the distributions of 
other grades, upon the assumption that ability in each grade is 
distributed in accordance with the normal surface of frequency, 
and that the values given in Table XXVIII are substantially 
correct. 

6. Referring All Sentences of Scale A to Zero 

Table XV gave the value of each sentence of Language Scale 
A for each elementary grade, and Table XVI gave their values 
for the higher grades. In Table XV, for instance, sentence No. 
7 had a positive value of 1.154 in the second grade and a value 
of — .203 in the third grade. Now we know from Table XXVIII 
that the second grade median is at i .687 P.E. and the third grade 
median at 3.286 P.E. above zero. 1.154 added to 1.687 gives 
this sentence a value of 2.841 above zero in the second grade, 
while .203 subtracted from 3.286 gives it a value of 3.083 above 
zero in the third grade. Table XXIX (page 56) is made from 
Table XV by employing in this way the values given in Table 
XXVIII for each grade median. 



Calculation of the Difficulty of Test Sentences 



55 



Pi 



56 



Completion-Test Language Scales 



TABLE XXIX 



Location Above Zebo of Each Sentence of Language Scale A for Each 
Elementary Grade. 1 = P.E. 



Sentence 


Grade 


Grade 


Grade 


Grade 


Grade 


Grade 


Grade 


] 


No. 


II 


III 


IV 


V 


VI 


VII 


VIII 


2 


2x 


.985 


1.355 


2.176 


2.908 


3.906 


4.321 


4.988 


4 


2y 


.928 


1.146 


1.902 


2.344 


3.068 


3.623 


4.439 


7 


3x 


2.841 


3.083 


3.437 


3.669 


3.915 


4.065 


4.666 


11 


3y 


2.855 


3.058 


3.392 


3.575 


3.930 


4.453 


4.774 


22 


4x 


3.948 


4.293 


4.276 


4.2.55 


4.529 


4.507 


4.866 


29 


4y 


3.843 


3.920 


4.106 


4.097 


4.295 


4.674 


4.782 


23 


5x 


4.261 


4.334 


4.714 


4.983 


5.344 


5.721 


5.971 


24 


5y 


4.167 


4.573 


5.021 


5.117 


5.374 


5.716 


5.867 


27 


6x 


4.622 


4.704 


5.173 


5.671 


6.182 


6.621 


7.060 


31 


6y 


4.922 


4.931 


5.128 


5.686 


5.951 


6.462 


6.900 


28 


7x 


4.941 


5.276 


5.635 


5.975 


6.265 


6.679 


7.086 


30 


7y 


5.421 


5.352 


5.614 


5.956 


6.294 


6.700 


6.995 


37 


8x 


6.124 


6.295 


6.275 


6.615 


6.853 


7.102 


7.566 


34 


8y 


5.789 


5.769 


6.077 


6.452 


6.648 


7.024 


7.302 


36 


9x 




7.542 


7.652 


7.803 


7.826 


7.828 


7.996 


43 


9y 




8.006 


7.869 


7.811 


7.790 


7.827 


7.959 


41 


lOx 




7.854 


7.267 


7.375 


7.602 


7.816 


7.949 


45 


lOy 




7.854 


8.055 


8.220 


8.350 


8.659 


8.700 


49 


llx 






9.090 


8.846 


8.923 


8.781 


8.788 


52 


iiy 






8.674 


9.176 


9.216 


9.016 


8.988 


53 


12x 






9.403 


9.389 


9.623 


9.688 


9.610 


55 


12y 






9.243 


9.433 


9.827 


9.758 


9.794 


54 


13x 






9.090 


9.823 


10.039 


10.312 


10.204 


56 


13y 








9.926 


10.262 


10.453 


10.422 


Grade Position . . 


1.687 


3.286 


4.523 


5.451 


6.295 


7.112 


7.757 



Table XXX shows the location above zero of each sentence in 
Language Scale A for each higher grade in the schools where both 
elementary and high school classes were tested. Table XXX is 
derived from Table XVI by employing the grade locations shown 
in Table XXVIII. 

The number of pupils in each of the higher grades which fur- 
nished the data for Table XXX was small, and yet these pupils 
were slightly more able than the pupils in the same grades of the 
large city high schools where a short completion test was given.. 
This means, probably, that for high school students in general 
the values assigned in Table XXX are too low. 

Six of the sentences actually were included in both sets of tests, 
and the location of each of these six sentences for each of the 
higher grades was shown in Table XX. Table XXXI gives the 



Calculation of the Difficulty of Test Sentences 
TABLE XXX 



57 



Location Above Zero op Each Sentence op Language Scale A for 
Each Higher Grade (Complete System Group.) 1=P.E. 





Sentence 
No. 


Grade 
IX 


Grade 
X 


Grade 
XI 


Grade 
XII 


Grade 
Col. Gr. 




2 


4.835 
5.344 

5.484 
5.678 

5.095 
5.095 

6.356 
6.561 

7.376 
7.021 

7.491 
7.334 

7.735 
7.823 

8.221 
8.000 

8.316 
8.765 

8.925 
9.275 

9.754 
10.107 

10.408 
10.804 


6.100 
5.318 

5.318 
5.818 

6.179 
5.928 

7.148 
6.988 

7.510 
7.566 

7.875 
7.919 

8.126 

7.874 

8.635 
8.486 

8.532 
9.118 

9.173 
9.206 

9.740 
9.902 

10.419 
11.090 


5.470 
5.839 

6.867 
6.982 

4.853 
6.058 

7.636 
6.867 

7.578 
7.303 

8.096 
8.096 

8.728 
8.158 

8.712 
8.504 

9.009 
9.024 

9.521 
9.508 

9.868 
10.043 

10.402 
10.894 


6.701 

5.933 
5.933 

7.880 
7.554 

8.067 
7.608 

8.460 
8.168 

8.538 
8.102 

8.886 
8.886 

8.661 
9.345 

9.288 
9.474 

10.037 
10.224 

11.043 
11.018 


8 493 




4 






7 


7 658 




11 


7 286 




22 






29 






23 


8 052 




24 


8 188 




27 


8 991 




31 


9.084 




28 


9 843 




30 


9 167 




37 


9 662 




34 


9 284 




36 


9.689 




43 

41 


8.833 
9.743 




45 


9.768 




49 


9.819 




52 


9.320 




53 


10.661 




65 


10.592 




54 


10.815 




56 


11.324 









location above zero of each of the six sentences for each high 
school grade, first as calculated from Table XXX, and second as 
determined from the larger number of pupils reported in Table 
XX. Table XXXI also shows the amount of difference between 
the two values for each sentence and the average amount of 
difference caused by the larger numbers from the city high schools. 
In order to correct the values shown in Table XXX for the 
slightly extraordinary abilities of the pupils from whom it was- 



58 



Completion-Test Language Scales 



TABLE XXXI 



Changes in Values Above Zeko of Six Sentences by Use on Larger 
Numbers of High School Students 



H. S. 


No. 
Pupils 


Sentence No. 


Average 
Differ- 
ence 


Grade 


37 


36 


45 


49 


55 


54 


IX 


273 
537 


7.735 

7.782 


8.221 
8.198 


8.765 
8.801 


8.925 
9.057 


10.107 
10.107 


10.408 
10.777 




X 


Difif. 

171 

402 


.047 

8.126 
8.290 


-.023 

8.635 

8.384 


.036 

9.118 
9.118 


.132 

9.173 
9.164 




9.902 
10.118 


.369 

10.419 
10.755 


.093 


XI 


Diff. 

136 
470 


.164 

8.728 
8.800 


-.251 

8.712 
8.800 




9.024 
9.370 


-.009 

9.521 
9.378 


.216 

10.043 
10.181 


.336 

10.402 
10.984 


.076 


XII 


Diff. 

103 
385 


.072 

8.538 
8.960 


.088 

8.886 
8.706 


.346 

9.345 
9.359 


-.143 

9.288 
9.314 


.138 

10.224 
10.081 


.582 

11.043 
10.992 


.180 




Diff. 


.422 


-.180 


.014 


.026 


-.143 


-.051 


.014 



derived, .09 was added to all values for grade IX, .07 to all grade 
X values, .15 in grade XI, and the values in grade XII were not 
changed at all. These corrections were determined by refer- 
ence to the average differences shown in Table XXXI. 

Having now located by each grade the distance above zero for 
each sentence of Scale A, we may undertake to determine what 
the location of each sentence is for school children in general. 
It will be noticed in Table XXIX that there is a tendency for 
each sentence to have a higher location in the higher grades than 
it has in the lower grades. This is probably due in part to the 
presence in these higher grades of a few inferior individuals, who 
fail to make satisfactory completions of sentences which should 
be easy for them. It would be unjust, however, to allow the few 
dull pupils who manage to get into the higher grades to keep on 
dragging these easy sentences into the higher ranges of the scale. 
Undoubtedly the most reliable distribution for determining the 
general difficulty of a sentence is the distribution whose median is 



Calculation of the Difficulty of Test Sentences 



59 



nearest to the position of the sentence. I have therefore given 
double weight to the determinations by those grade distributions 
whose medians were not more than i P.E. from the sentence's 
location, and single weight to all determinations by grades more 
than I P.E. but less than 2.5 P.E. from the sentence. 

Fig. 18 shows how a grade distribution would affect sentences 
at various distances. 




-2.5f£. 



Fig. 18. 



Showing the Influence Allowed Various Parts of a Distribution in 
Determining the General Location of a Sentence. 



The determination of a distribution is given double weight if its median 
is within i P.E. of a sentence, single weight if more than i and less than 
2.5 P.E., and no weight at all in the general determination if its median 
is more than 2.5 P.E. from the sentence. Areas c and / are not allowed to 
help determine the general difficulty of a sentence. 

Table XXXII shows for the first five sentences the details of 
just how the weighting was done. 



TABLE XXXII 

Determination of General Locations op Sentences 



Distribution 


Sentences No. 


2 


4 


7 


11 


22 


II 

III 

IV 

V 
VI 

VII 


.985 
.985 

1.355 
2.176 


.928 
.928 

1.146 


2.841 

3.083 
3.083 

3.437 

3.669 
3.915 


2.855 

3.058 
3.058 

3.392 

3.575 
3.930 


3.948 

4.293 

4.276 
4.276 

4.255 

4.529 


Average 

Use 


1.376 
1.38 


1.000 
1.00 


3.338 
3.34 


3.311 
3.31 


4.263 
4.26 







6o Completion-Test Language Scales 

Weighting in this manner the values shown in Tables XXIX 
and XXX (after raising the values of Table XXX by the amounts 
determined in Table XXXI), the figures obtained to show the 
general difficulty of each sentence for all grades are shown in 
Table XXXIII. 

TABLE XXXIII 

Final Values of Sentences in Scale A 

Sentence General 

No.i Value 

4 1.00 

2 1.38 

11 3.31 

7 3.34 

29 4.12 

22 4.26 

23 5.40 

24 5.69 

31 6.50 

27 6.67 

30 6.95 

28 7.04 

34 7.31 

37 7.85 

43 8.29 

36 8.32 

41 8.37 

45 9.04 

49 9.20 

52 9.29 

53 10.05 

55 10.19 

54 10.76 

56 11.17 



^Sentences are here in the order of difficulty, not the order of Scale A. 



Calculation of the Difficulty of Test Sentences 6i 

7. Estimation of the Difficulty of Other Sentences^ 

Scale A is the basis upon which all values are built in this 
study. The Graded Series of test sentences was given to a 
smaller number of children and was not given to the College 
Graduate group, so there are two corrections to be made in the 
figures obtained directly from its use : a correction must first be 
made for any difference in the abilities of the groups which are 
called by the same grade number, and a second correction must 
be made in the values of the more difficult sentences for the lack 
of the College Graduate group. The other lists of tests outside 
of the Graded Series require the same corrections, except that 
in the cases of these others the second correction is not simply for 
the lack of one grade group but for the lack of several such groups. 

Lack of sufficient numbers of children tested to actually locate 
the difficulty of a test can not be corrected, except by testing a 
sufficient number of children. The writer feels that the irregu- 
larities due to small numbers are negligible in the sentences of 
Scale A, very small in the other sentences of the Graded Series, 
somewhat larger in the sentences numbered from 57 to 72, and 
still larger in those sentences numbered higher than 72. For the 
sentences numbered above 56, it can only be said that their diffi- 
culty has been estimated carefully, although much more statistical 
labor has been spent upon them than upon the sentences of Scale 
A. To actually measure the difficulty of a sentence requires 
that it be tried upon hundreds of children in each grade. No 
amount of calculation can take the place of large numbers of 
children tested. 

Table XXXIV gives the score made upon each sentence of the 
Graded Series in each school grade. Table XXXV gives the P.E. 
equivalents of the score, and Table XXXVI gives the resulting 
location above zero of each sentence. 



^ Other sentences than those included in the Language Scales are not given 
in the body of this report, but each sentence used in this investigation, together 
with the scheme used in scoring it, will be found in the Appendix. 



62 



Completion-Test Language Scales 



TABLE XXXIV 
Score Made by Each Grade on Each Sentence of the Graded Series 



Sentence 


Grade 


Grade 


Grade 


Grade 


Grade 


Grade 


Grade 


Grade 


Grade 


Grade 


Grade 


No. 


II 


III 


IV 


V 


VI 


VII 


VIII 


IX 


X 


XI 


XII 


1 


990 


1397 


1357 


1467 


1142 


1207 


874 


384 


241 


211 


163 


2 


970 


1346 


1293 


1422 


1095 


1199 


862 


381 


236 


211 


166 


3 


675 


1056 


1050 


1273 


1003 


1124 


832 


369 


235 


200 


159 


4 


967 


1382 


1303 


1466 


1134 


1213 


874 


374 


240 


210 


163 


5 


476 


1056 


1159 


1407 


1132 


1214 


882 


383 


242 


210 


164 


6 


695 


1141 


1270 


1475 


1145 


1226 


888 


383 


242 


212 


166 


7 


300 


811 


1014 


1324 


1077 


1203 


872 


373 


240 


201 


166 


8 


448 


924 


1053 


1370 


1076 


1177 


865 


372 


240 


210 


164 


9 


290 


754 


886 


1230 


1014 


1114 


850 


376 


235 


207 


163 


10 


354 


797 


933 


1273 


1066 


1179 


858 


377 


234 


206 


162 


11 


308 


801 


1011 


1317 


1078 


1166 


862 


366 


237 


201 


165 


12 


273 


803 


1014 


1264 


1037 


1140 


853 


370 


239 


210 


158 


13 


183 


603 


809 


1163 


1003 


1157 


868 


363 


237 


210 


164 


14 


216 


684 


867 


1200 


942 


1061 


784 


354 


228 


182 


160 


15 


119 


499 


695 


1005 


904 


1057 


799 


366 


230 


207 


157 


16 


157 


603 


816 


1207 


974 


1125 


836 


375 


233 


204 


161 


17 


248 


762 


934 


1238 


1038 


1165 


861 


374 


238 


212 


166 


18 


118 


480 


754 


1066 


954 


1064 


805 


374 


236 


207 


158 


19 


239 


788 


894 


1183 


986 


1037 


802 


360 


232 


202 


158 


20 


159 


615 


900 


1192 


1008 


1101 


836 


377 


237 


209 


162 


21 


112 


523 


784 


1115 


950 


1029 


788 


369 


234 


209 


160 


22 


46 


346 


713 


1102 


961 


1166 


855 


376 


236 


212 


165 


23 


53 


327 


489 


809 


738 


911 


765 


340 


213 


189 


148 


24 


79 


261 


397 


783 


755 


924 


783 


338 


222 


204 


155 


26 


52 


355 


491 


881 


759 


846 


655 


295 


191 


169 


125 


26 


59 


325 


462 


729 


608 


750 


587 


271 


179 


149 


120 


27 


29 


256 


420 


589 


567 


697 


604 


272 


208 


189 


147 


28 


14 


122 


248 


468 


531 


676 


593 


265 


185 


173 


133 


29 


49 


469 


759 


1191 


1040 


1160 


867 


378 


238 


211 


166 


30 


8 


134 


240 


517 


482 


674 


598 


283 


183 


172 


145 


31 


16 


194 


437 


563 


623 


664 


569 


321 


210 


198 


151 


32 


2 




11 


20 


76 


161 


187 


167 


127 


126 


102 


33 




14 


43 


143 


201 


404 


392 


176 


142 


121 


106 


34 


5 


53 


137 


297 


414 


564 


551 


236 


192 


173 


144 


35 


6 


73 


149 


304 


344 


554 


508 


239 


177 


162 


126 


36 




6 


20 


56 


149 


270 


329 


*476 


♦422 


♦342 


•377 


37 




3 


88 


223 


324 


523 


445 


♦578 


♦425 


•313 


•321 


38 






25 


81 


184 


373 


341 


*451 


♦370 


•294 


♦308 


39 




1 


13 


64 


152 


343 


375 


*439 


♦351 


•287 


•300 


40 






15 


61 


150 


293 


345 


♦452 


•361 


♦306 


•345 


41 






28 


77 


120 


269 


302 


♦362 


♦350 


•285 


♦312 


42 






5 


25 


117 


273 


266 


♦370 


♦311 


•245 


♦287 


43 






5 


41 


120 


280 


361 


♦480 


♦431 


♦345 


♦355 


44 




1 


20 


53 


88 


178 


260 


♦324 


♦310 


♦255 


•273 


45 






4 


43 


99 


154 


232 


♦339 


♦307 


♦278 


♦307 


46 








10 


39 


127 


180 


♦333 


♦331 


♦261 


♦302 


47 






4 


19 


39 


140 


193 


♦333 


♦352 


•263 


♦286 


48 






2 


8 


19 


95 


180 


♦206 


♦234 


•202 


♦243 


49 






1 


4 


19 


103 


158 


♦271 


•272 


♦220 


•297 


50 






3 


20 


43 


127 


191 


♦295 


•294 


♦219 


•242 


61 






2 


7 


15 


72 


92 


♦203 


♦209 


•167 


•208 


52 






2 


11 


17 


49 


99 


♦214 


♦284 


•233 


•269 


53 








3 


7 


41 


82 


♦152 


♦188 


♦185 


♦222 


54 












6 


24 


♦45 


•75 


♦87 


•97 


55 








2 


4 


22 


64 


♦106 


♦131 


♦154 


•203 


56 










1 


3 


21 


♦34 


♦49 


♦71 


•87 


Number 


770 


770 


695 


758 


579 


615 


444 


192 


121- 


106 


83 


tested . . . 
















♦456 


♦310 


•236 


♦229 


Perfect 


1540 


1540 


1390 


1516 


1158 


1230 


888 


384 


242 


212 


166 


Score . . . 
















"■912 


♦620 


•472 


♦458 



Calculation of the Difficulty of Test Sentences 



63 



TABLE XXXV 

P.E. Equivalents of Difference Between 50 Per Cent and Per Cent op 

Perfect Score Made by Each Grade for Each Sentence 

OF THE Graded Series 



Sentence 


Grade 


Grade 


Grade 


Grade 


Grade 


Grade 


Grade 


Grade 


Grade 


Grade 


Grade 


No. 


II 


III 


IV 


V 


VI 


VII 


VIII 


IX 


X 


XI 


XII 


1 


— .54 


—1.96 


—2.93 


-2.75 


—3.26 


—3.08 


—3.18 




—3.94 


—3.82 


—3.11 


2 


— .49 


-1.70 


-2.19 


—2.28 


—2.38 


—2.90 


—2.81 


—3.57 


—2.90 


—3.82 




3 


.23 


— .72 


—1.02 


—1.47 


—1.64 


—2.03 


—2.27 


—2.61 


—2.81 


—2.34 


—2.56 


4 


— .48 


—1.87 


—2.27 


—2.73 


—3.01 


—3.26 


—3.18 


—2.88 


—3.67 


—3.61 


-3.11 


5 


.74 


— .72 


—1.43 


—2.17 


—2.96 


—3.30 


—3.64 


-4.27 




—3.61 


—3.35 


6 


.18 


— .95 


—2.02 


—2.86 


—3.39 


—4.08 




-4.27 








7 


1.27 


— .10 


— .90 


—1.69 


—2.19 


—2.99 


—3.11 


—2.83 


—3.67 


-2.41 




8 


.82 


— .38 


—1.03 


—1.93 


—2.18 


—2.55 


—2.88 


—2.77 


—3.67 


—3.61 


-3.35 


9 


1.31 


.04 


— .52 


—1.31 


—1.71 


—1.95 


—2.55 


—3.01 


—2.81 


—2.93 


-3.11 


10 


1.10 


— .06 


— .66 


-1.47 


—2.08 


—2.58 


—2.71 


—3.11 


—2.73 


—2.83 


—2.93 


11 


1.25 


— .07 


— .90 


—1.66 


—2.20 


-2.41 


—2.81 


—2.48 


—3.01 


—2.41 


—3.72 


12 


1.37 


— .08 


— .90 


—1.44 


—1.87 


—2.16 


—2.61 


—2.67 


—3.36 


—3.61 


—2.47 


13 


1.75 


.41 


— .31 


—1.08 


—1.64 


—2.32 


—2.99 


—2.37 


—3.01 


—3.61 


—3.35 


14 


1.60 


.21 


— .47 


—1.20 


—1.32 


—1.62 


—1.76 


—2.10 


—2.33 


—1.59 


—2.67 


15 


2.11 


.68 


0.00 


— .62 


—1.15 


—1.59 


—1.90 


—2.45 


—2.44 


—2.93 


—2.38 


16 


1.89 


.41 


— .33 


—1.23 


—1.48 


—2.03 


—2.32 


—2.96 


—2.65 


—2.63 


—2.79 


17 


1.47 


.02 


— .66 


—1.34 


—1.87 


—2.40 


—2.79 


—2.88 


—3.15 






18 


2.11 


.73 


— .16 


— .79 


—1.38 


—1.64 


—1.96 


—2.88 


—2.93 


—2.93 


—2.47 


19 


1.51 


— .04 


— .54 


—1.14 


—1.54 


—1.49 


—1.93 


—2.28 


—2.58 


—2.48 


—2.47 


20 


1.87 


.38 


— .56 


—1.18 


—1.67 


—1.86 


—2.32 


—3.11 


—3.01 


—3.26 


—2.93 


21 


2.15 


.61 


— .24 


— .93 


—1.36 


—1.46 


—1.79 


—2.61 


—2.73 


—3.26 


—2.67 


22 


2.81 


1.12 


— .05 


— .89 


—1.41 


—2.41 


—2.65 


—3.01 


—2.90 




—3.72 


23 


2.71 


1.19 


.56 


— .13 


— .52 


— .96 


—1.54 


—1.78 


—1.74 


—1.83 


—1.83 


24 


2.42 


1.41 


.84 


— .06 


— .58 


—1.00 


—1.76 


—1.74 


—2.05 


—2.63 


—2.23 


25 


2.71 


1.09 


.56 


— .30 


— .59 


— .73 


— .94 


—1.09 


-1.19 


—1.23 


—1.01 


26 


2.63 


1.19 


.64 


.07 


— .09 


— .41 


— .62 


— .79 


— .95 


— .79 


- .88 


27 


3.08 


1.44 


.77 


.42 


.04 


— .25 


— .69 


- .81 


—1.69 


—1.83 


—1.79 


28 


3.51 


2.09 


1.37 


.74 


.16 


— .19 


— .64 


— .73 


—1.07 


—1.33 


—1.25 


29 


2.75 


.76 


— .17 


—1.18 


—1.88 


—2.34 


—2.96 


—3.18 


—3.18 


—3.82 




30 


3.82 


2.02 


1.40 


.61 


.31 


— .18 


— .66 


— .94 


—1.03 


—1.31 


—1.69 


31 


3.45 


1.71 


.72 


.49 


— .14 


— .16 


— .53 


—1.45 


—1.66 


—2.23 


-1.99 


32 


4.60 




3.67 


3.30 


2.23 


1.66 


1.19 


.24 


— .09 


— .36 


— .43 


33 




3.51 


2.77 


1.95 


1.40 


.66 


.22 


.16 


— .33 


— .26 


— .53 


34 


4.08 


2.71 


1.92 


1.27 


.54 


.16 


— .46 


— .43 


—1.21 


—1.33 


—1.65 


35 


3.94 


2.48 


1.84 


1.25 


.79 


.19 


— .27 


— .46 


— .91 


—1.07 


—1.04 


36 




3.94 


3.26 


2.66 


1.68 


1.15 


.49 


— .08 


— .70 


— .88 


—1.37 


37 




4.27 


2.27 


1.56 


.87 


.28 


.00 


— .51 


— .71 


— .62 


— .78 


38 






3.11 


2.40 


1.48 


.76 


.44 


.02 


— .36 


— .46 


— .66 


39 




4.60 


3.51 


2.56 


1.66 


.87 


.29 


.07 


— .25 


— .41 


— .59 


40 






3.39 


2.60 


1.68 


1.06 


.42 


.01 


— .30 


— .55 


-1.01 


41 






3.04 


2.42 


1.87 


1.15 


.61 


.39 — .24 


— .39 


— .70 


42 






3.94 


3.18 


1.89 


1.13 


.83 


.35 


— .01 


— .07 


- .48 


43 






3.94 


2.86 


1.87 


1.10 


.39 


— .10 


— .76 


— .91 


—1.12 


44 




4.60 


3.26 


2.69 


2.12 


1.57 


.81 


.65 




— .15 


— .36 


45 






4.08 


2.83 


2.03 


1.71 


.95 


.48 


.02 


— .33 


— .65 


46 








3.64 


2.71 


1.87 


1.23 


.61 


— .13 


— .20 


- .61 


47 






4.08 


3.35 


2.71 


1.79 


1.16 


.61 


— .25 


— .21 


— .47 


48 






4.60 


3.82 


3.18 


2.11 


1.23 


1.11 


.46 


.27 


— .11 


49 






4.60 


4.27 


3.18 


2.04 


1.37 


.79 


.23 


.13 


— .56 


50 






4.27 


3.30 


2.65 


1.87 


1.17 


.68 


.10 


.13 


— .10 


51 






4.60 


3.94 


3.22 


2.33 


1.87 


1.13 


.62 


.64 


.17 


52 






4.60 


3.64 


3.22 


2.60 


1.80 


1.07 


.16 


.02 


— .33 


53 








4.27 


3.72 


2.73 


1.97 


1.43 


.76 


.41 


.06 


54 












3.82 


2.86 


2.45 


1.73 


1.33 


1.19 


55 








4.60 


3.94 


3.11 


2.17 


1.77 


1.19 


.67 


.21 


56 










4.60 


4.27 


2.93 


2.65 


2.09 


1.54 


1.30 


Grade 
























Position. 


1.69 


3.29 


4.52 


5.45 


6.29 


7.11 


7.76 


8.33 


9.06 


9.45 


9.76 



H 



Completion-Test Language Scales 



TABLE XXXVI 

Location Above Zero Shown by Each Grade for Each Sentence of the 
Graded Series 1 = P.E. 



Sentence 


Grade 


Grade 


Grade 


Grade 


Grade 


Grade 


Grade 


Grade 


Grade 


Grade 


Grade 


No. 


II 


III 


IV 


V 


VI 


VII 


VIII 


IX 


X 


XI 


XII 


1 


1.15 


1.33 


1.59 


2.70 


3.03 


4.03 


4.58 




5.11 


5.63 


6.65 


2 


1.20 


1.59 


2.33 


3.17 


3.91 


4.21 


4.95 


4.76 


6.15 


5.63 




3 


1.92 


2.57 


3.50 


3.98 


4.65 


5.08 


5.49 


5.72 


6.24 


7.11 


7.20 


4 


1.21 


1.42 


2.25 


2.72 


3.28 


3.85 


4.58 


5.45 


5.48 


5.94 


6.65 


6 


2.43 


2.57 


«.09 


3.28 


3.33 


3.81 


4.12 


4.06 




5.94 


6.41 


6 


1.87 


2.34 


2.50 


2.59 


2.90 


3.03 




4.06 








7 


2.96 


3.19 


3.62 


3.76 


4.10 


4.12 


4.65 


5.50 


5.48 


7.04 




8 


2.51 


2.91 


3.49 


3.52 


4.11 


4.56 


4.88 


5.56 


5.48 


5.94 


6.41 


9 


3.00 


3.33 


4.00 


4.14 


4.58 


5.16 


5.21 


5.32 


6.24 


6.52 


6.65 


10 


2.79 


3.23 


3.86 


3.98 


4.21 


4.53 


5.05 


5.22 


6.32 


6.62 


6.83 


11 


2.94 


3.22 


3.62 


3.79 


4.09 


4.70 


4.95 


5.85 


6.04 


7.04 


6.04 


12 


3.06 


3.21 


3.62 


4.01 


4.42 


4.96 


5.15 


5.66 


5.70 


5.94 


7.29 


13 


3.44 


3.70 


4.21 


4.37 


4.65 


4.79 


4.77 


5.96 


6.04 


5.94 


6.41 


14 


3.29 


3.50 


4.05 


4.25 


4.97 


5.49 


6.00 


6.23 


6.72 


7.86 


7.09 


15 


3.80 


3.97 


4.52 


4.83 


5.14 


5.52 


5.86 


5.88 


6.61 


6.52 


7.38 


16 


3.58 


3.70 


4.19 


4.22 


4.81 


5.08 


5.44 


5.37 


6.40 


6.82 


6.97 


17 


3.16 


3.31 


3.86 


4.11 


4.42 


4.71 


4.97 


5.45 


5.90 






18 


3.80 


4.02 


4.36 


4.66 


4.91 


5.47 


5.80 


5.45 


6.12 


6.52 


7.29 


19 


3.20 


3.25 


3.98 


4.31 


4.75 


5.62 


5.83 


6.05 


6.47 


6.97 


7.29 


20 


3.56 


3.67 


3.96 


4.27 


4.62 


5.25 


5.44 


5.22 


6.04 


6.19 


6.83 


21 


3.84 


3.90 


4.28 


4.52 


4.93 


5.65 


5.97 


5.72 


6.32 


6.19 


7.09 


22 


4.50 


4.41 


4.47 


4.56 


4.88 


4.70 


5.11 


5.32 


6.15 




6.04 


23 


4.40 


4.48 


5.08 


5.32 


5.77 


6.15 


6.22 


6.55 


7.31 


7.62 


7.93 


24 


4.11 


4.70 


5.36 


5.39 


5.71 


6.11 


6.00 


6.59 


7.00 


6.82 


7.53 


25 


4.40 


4.38 


5.08 


5.15 


5.70 


6.38 


6.82 


7.24 


7.86 


8.22 


8.75 


26 


4.32 


4.48 


5.16 


5.52 


6.20 


6.70 


7.14 


7.54 


8.10 


8.66 


8.88 


27 


4.77 


4.73 


5.29 


5.87 


6.33 


6.86 


7.07 


7.52 


7.46 


7.62 


7.97 


28 


5.20 


5.38 


5.89 


6.19 


6.45 


6.92 


7.12 


7.60 


7.98 


8.12 


8.51 


29 


4.44 


4.05 


4.35 


4.27 


4.41 


4.77 


4.80 


5.15 


5.87 


5.63 




30 


5.51 


5.31 


5.92 


6.06 


6.60 


6.93 


7.10 


7.39 


8.02 


8.14 


8.07 


31 


5.14 


5.00 


5.24 


5.94 


6.15 


6.96 


7.23 


6.88 


7.39 


7.22 


7.77 


32 


6.29 




8.09 


8.75 


8.52 


8.77 


8.95 


8.57 


8.96 


9.10 


9.33 


33 




6.80 


7.29 


7.40 


7.69 


7.77 


7.98 


8.49 


8.72 


9.19 


9.23 


34 


5.77 


6.00 


6.44 


6.72 


6.83 


7.27 


7.30 


7.90 


7.84 


8.12 


8.11 


35 


5.63 


5.77 


6.36 


6.70 


7.08 


7.30 


7.49 


7.87 


8.14 


8.38 


8.72 


36 




7.23 


7.78 


8.10 


7.97 


8.26 


8.25 


8.25 


8.35 


8.57 


8.39 


37 




7.56 


6.79 


7.01 


7.16 


7.39 


7.76 


7.82 


8.34 


8.83 


8.98 


38 






7.63 


7.85 


7.77 


7.87 


8.20 


8.35 


8.69 


8.99 


9.10 


39 




7.89 


8.03 


8.01 


7.95 


7.98 


8.05 


8.40 


8.80 


9.04 


9.17 


40 






7.91 


8.05 


7.97 


8.17 


8.18 


8.34 


8.75 


8.90 


8.75 


41 






7.56 


7.87 


8.16 


8.26 


8.37 


8.72 


8.81 


9.06 


9.06 


42 






8.46 


8.63 


8.18 


8.24 


8.59 


8.68 


9.04 


9.38 


9.28 


43 






8.46 


8.31 


8.16 


8.21 


8.15 


8.23 


8.29 


8.54 


8.64 


44 




7.89 


7.78 


8.14 


8.41 


8.68 


8.57 


8.88 


9.05 


9.30 


9.40 


45 






8.60 


8.28 


8.32 


8.82 


8.71 


8.81 


9.07 


9.12 


9.11 


46 








9.09 


9.00 


8.98 


8.99 


8.84 


8.92 


9.25 


9.15 


47 






8.60 


8.80 


9.00 


8.90 


8.92 


8.84 


8.80 


9.24 


9.29 


48 






9.12 


9.27 


9.47 


9.22 


8.99 


9.44 


9.51 


9.72 


9.65 


49 






9.12 


9.72 


9.47 


9.15 


9.13 


9.12 


9.28 


9.58 


9.20 


50 






8.79 


8.75 


8.94 


8.98 


8.93 


9.01 


9.15 


9.58 


9.66 


51 






9.12 


9.39 


9.51 


9.44 


9.63 


9.46 


9.67 


10.09 


9.93 


52 






9.12 


9.09 


9.51 


9.71 


9.56 


9.40 


9.21 


9.47 


9.43 


53 








9.72 


10.01 


9.84 


9.73 


9.76 


9.81 


9.86 


9.82 


54 












10.93 


10.62 


10.78 


10.78 


10.78 


10.95 


55 








10.05 


10.23 


10.22 


9.93 


10.10 


10.24 


10.12 


9.97 


56 










10.89 


11.38 


10.69 


10.98 


11.14 


10.99 


11.06 


Grade 
























Position . 


1.69 


3.29 


4.52 


5.45 


6.29 


7.11 


7.76 


8.33 


9.05 


9.45 


9.76 



The corrections for the results of the Graded Series, to com- 
pensate for the low ability shown by those who were tested with 
the entire Graded Series as compared with those tested by Scale 



Calculation of the Difficulty of Test Sentences 



65 



A only, are determined from Table XXXVII, which shows the 
differences, for each sentence of Language Scale A, between the 
results obtained in the Graded Series alone and the results ob- 
tained from all pupils who were tested with the sentences of 
Language Scale A. Table XXXVII is obtained by taking the 
difference on each sentence between the values shown in Table 
XXXVI and those shown in Tables XXIX and XXX. 

TABLE XXXVII 

Change op Location Above Zero Made in Each Sentence of the 
Graded Series by its Inclusion in Language Scale A 



Sentence 


Grade 


Grade 


Grade 


Grade 


Grade 


Grade 


Grade 


Grade 


Grade 


Grade 


Grade 


No. 


II 


III 


IV 


V 


VI 


VII 


VIII 


IX 


X 


XI 


XII 


2 


— .22 


— .24 


— .15 


— .26 





.11 


.04 


.16 


.02 


— .01 




4 


— .28 


— .27 


— .35 


— .38 


— .21 


— .23 


— .14 


— .02 


— .09 


.05 


.05 


7 


— .12 


— .11 


— .18 


— .09 


— .19 


— .06 


.02 


.07 


— .09 


— .02 




11 


— .09 


— .16 


— .23 


— .22 


— .16 


— .25 


— .18 


— .08 


— .15 


.09 


-.11 


22 


— .55 


— .12 


— .19 


— .31 


— .36 


— .19 


— .24 


— .14 


.10 




— .11 


23 


— .14 


— .15 


— .37 


— .34 


— .43 


— .43 


— .25 


— .10 


— .09 


.17 


— .05 


24 


.06 


— .13 


— .34 


— .27 


— .34 


— .39 


— .13 


.06 


.06 


.20 


.02 


27 


— .16 


— .03 


— .12 


— .20 


— .15 


— .24 


— .01 


— .05 


.12 


.11 


.10 


28 


— .26 


— .10 


— .26 


— .22 


— .19 


— .24 


— .03 


-.02 


— .04 


.13 


— .05 


29 


-.60 


— .13 


-.24 


— .17 


— .12 


— .10 


— .02 


.03 


.13 


.68 




30 


-.09 


.04 


-.31 


— .10 


— .31 


— .23 


— .11 


.03 


— .03 


.11 


.10 


31 


— .22 


— .07 


— .11 


— .25 


— .20 


— .50 


— .33 


.23 


.25 


.23 


—.16 


34 


.02 


— .23 


— .36 


— .27 


— .18 


— .25 





.01 


.10 


.19 


—.01 


36 




.31 


— .13 


— .30 


— .14 


— .43 


— .25 


— .06 


.03 


.23 


.32 


37 




—1.27 


— .52 


— .40 


— .31 


— .29 


— .19 


— .04 


— .05 


— .03 


—.02 


41 






— .29 


— .50 


— .66 


— .44 


— .42 


— .31 


— .21 


.10 


-.40 


43 






— .69 


— .50 


— .37 


— .38 


— .19 


— .14 


.27 


.11 


.25 


45 






— .55 


— .06 


.03 


— .16 


— .01 


— .01 


.05 


.25 


.25 


49 






— .03 


— .87 


— .65 


— .37 


— .34 


— .06 


— .12 


— .05 


.11 


52 






—.45 


.09 


— .29 


-.69 


— .57 


— .04 


.07 


— .11 


.04 


53 








— .33 


— .39 


— .15 


— .12 


.08 





.16 


.22 


54 












— .62 


— .42 





— .03 


.20 


.04 


65 








— .62 


— .40 


— .46 


— .14 


.01 


— .12 


.06 


.11 


66 










— .63 


— .93 


— .27 


-.09 


.02 


.05 


— .04 


Below — 1. 




— .25 


— .25 


— .22 


— .17 


— .16 


— .11 


+ .02 


+ .02 


+ .15 


+ .03 


—1. to +1. 


— .25 


— .13 


— .22 


— .24 


— .26 


— .31 


— .15 


— .06 


.00 


+ .08 


+ .04 


Above +1. 


— .20 


— .17 


— .35 


— .38 


— .41 


— .46 


— .31 


— .01 









The changes indicated in Table XXXVII are not averaged as 
they were in the case of Table XXXI, but are grouped according 
to the nearness of the median of the distribution concerned to the 
sentence in question. All changes upon sentences more than I 
P.E. below the median are put into one group, all those upon 
sentences from i P.E. below to i P.E. above are put into another 
group, and those upon sentences more than i P.E. above are 
put into a third group, and each group is averaged. The aver- 
ages of the groups are then used to correct the values of the 



66 



Completion-Test Language Scales 



sentences which were not given in Scale A, the corrections being 
applied within the same limits as were used in obtaining them. 
The result of employing these average changes as corrections is 
shown in Table XXXVIII. 

TABLE XXXVIII 

Estimated Location Above Zero op Each Sentence Given in the 
Graded Series Only 



Sentence 


Grade 


Grade 


Grade 


Grade 


Grade 


Grade 


Grade 


Grade 


Grade 


Grade 


Grade 


. No. 


II 


III 


IV 


V 


VI 


VII 


VIII 


IX 


X 


XI 


XII 


1 


.90 


1.08 


1.34 


2.48 


2.86 


3.87 


4.47 




6.13 


5.78 


6.68 


3 


1.67 


2.44 


3.25 


3.76 


4.48 


4.92 


5.38 


5.74 


6.26 


7.26 


7.23 


5 


2.18 


2.44 


2.84 


3.06 


3.16 


3.65 


4.01 


4.08 




6.09 


6.44 


6 


1.62 


2.21 


2.25 


2.37 


2.73 


2.87 




4.08 








8 


2.26 


2.78 


3.24 


3.30 


3.94 


4.40 


4.77 


5.58 


5.50 


6.09 


6.44 


9 


2.80 


3.20 


3.78 


3.92 


4.41 


5.00 


5.10 


5.34 


6.26 


6.67 


6.68 


10 


2.59 


3.10 


3,64 


3.76 


4.04 


4.37 


4.94 


5.24 


6.34 


6.77 


6.86 


12 


2.86 


3.08 


3.40 


3.79 


4.25 


4.80 


5.04 


5.68 


5.72 


6.09 


7.32 


13 


3.24 


3.67 


3.99 


4.16 


4.48 


4.63 


4.66 


5.98 


6.06 


6.09 


6.44 


14 


3.09 


3.37 


3.83 


4.03 


4.80 


6.33 


5.89 


6.25 


6.74 


8.01 


7.12 


15 


3.60 


3.84 


4.30 


4.59 


4.97 


5.36 


5.76 


5.90 


6.63 


6.67 


7.41 


16 


3.38 


3.57 


3.97 


4.00 


4.64 


4.92 


5.33 


6.39 


6.42 


6.97 


7.00 


17 


2.96 


3.18 


3.64 


3.89 


4.25 


4.55 


4.86 


5.47 


5.92 






18 


3.60 


3.89 


4.14 


4.42 


4.74 


5.31 


5.69 


5.47 


6.14 


6.67 


7.32 


19 


3.00 


3.12 


3.76 


4.09 


4.68 


5.46 


6.72 


6.07 


6.49 


7.12 


7.32 


20 


3.36 


3.64 


3.74 


4.05 


4.45 


5.09 


5.33 


5.24 


6.06 


6.34 


6.86 


21 


3.64 


3.77 


4.06 


4.28 


4.76 


5.49 


5.86 


5.74 


6.34 


6.34 


7.12 


25 


4.20 


4.21 


4.86 


4.91 


5.44 


6.07 


6.67 


7.26 


7.88 


8.37 


8.78 


26 


4.12 


4.31 


4.94 


5.28 


5.94 


6.39 


6.99 


7.48 


8.12 


8.81 


8.92 


32 


6.09 




7.74 


8.37 


8.11 


8.31 


8.64 


8.51 


8.96 


9.18 


9.37 


33 




6.63 


6.94 


7.02 


7.28 


7.46 


7.83 


8.43 


8.72 


9.27 


9.27 


35 


5.43 


5.60 


6.01 


6.32 


6.82 


6.99 


7.34 


7.81 


8.14 


8.63 


8.75 


38 






7.28 


7.47 


7.36 


7.56 


8.05 


8.29 


8.69 


9.07 


9.14 


39 




7.72 


7.68 


7.63 


7.54 


7.67 


7.90 


8.34 


8.80 


9.12 


9.21 


40 






7.66 


7.67 


7.66 


7.71 


8.03 


8.28 


8.75 


8.98 


8.78 


42 






8.11 


8.25 


7.77 


7.78 


8.44 


8.62 


9.04 


9.46 


9.32 


44 




7.72 


7.43 


7.76 


8.00 


8.22 


8.42 


8.82 


9.05 


9.38 


9.44 


46 








8.71 


8.59 


8.52 


8.68 


8.78 


8.92 


9.33 


9.19 


47 






8.25 


8.42 


8.69 


8.44 


8.61 


8.78 


8.80 


9.32 


9.33 


48 






8.77 


8.89 


9.06 


8.76 


8.68 


9.43 


9.61 


9.80 


9.69 


50 






8.44 


8.37 


8.53 


8.52 


8.62 


8.95 


9.16 


9.66 


9.70 


51 






8.77 


9.01 


9.10 


8.98 


9.32 


9.45 


9.67 


10.17 


9.97 



The general difficulty of the Graded Series tests was calculated 
from Table XXXVIII in exactly the same way as the general 
values of the sentences in Scale A were calculated from Tables 
XXIX and XXX. 

The amount of compensation for the lack of the College Grad- 
uate group was determined by finding what the value of the more 
difficult tests in Scale A would have been if the values from this 
superior group had not been used in calculating the general 
difficulty of the sentences. It was found that the College Grad- 
uate group had not influenced the general value of any Scale A 
sentence receiving a general value of less than 6.oo P.E. The 



Calculation of the Difficulty of Test Sentences 67 

sentences which without the C.G. group would have been located 
between 6.00 and 7.00 had been raised on the average .16 P.E. 
by the use of the C.G. group. Those sentences which had re- 
ceived between 7.00 and 8.00 had been raised .13; between 8.00 
and 9.00, .08; between 9.00 and 10.00, .07; and above 10.00, .07. 
These averages were therefore applied as corrections to the gen- 
eral determinations for the Graded Series sentences, each aver- 
age being applied to the range within which it had been found. 
The final values obtained after all the corrections had been 
made are shown in Table XXXIX. 

TABLE XXXIX 

Final Values of Sentences Given in the Graded Series Only 

Sent. No. Value 

1 .96 

3 3.33 

5 2.52 

6 1.98 

8 2.94 

9 3.76 
10 3.41 

12 3.58 

13 4.03 

14 4.88 
16 4.81 

16 4.15 

17 3.66 

18 4.42 

19 4.47 

20 4.09 

21 4.40 

25 6.32 

26 7.00 

32 8.91 

33 8.38 
35 7.42 

38 8.42 

39 8.58 

40 8.46 
42 8.86 
44 8.95 

46 9.04 

47 9.03 

48 9.50 

50 9.28 

51 9.78 



68 



Completion-Test Language Scales 



TABLE XL 

The Score Made on Each Sentence of the Intermediate Schooi. Series 



Sentence 


Grade 


Grade 


Grade 


Grade 


Grade 


Grade 


No. 


III 


IV 


V 


VI 


VII 


VIII 


2 


287 


676 


741 


1046 


1289 


1726 


4 


302 


704 


760 


1083 


1336 


1762 


7 


241 


638 


710 


1044 


1315 


174S 


11 


224 


624 


714 


1036 


1309 


1747 


22 


129 


512 


676 


1018 


1308 


1746 


29 


149 


519 


646 


995 


1284 


1744 


23 


115 


424 


553 


866 


1203 


1604 


24 


97 


369 


522 


843 


1170 


1613 


27 


97 


272 


365 


605 


902 


1199 


31 


53 


271 


363 


604 


987 


1317 


28 


54 


196 


346 


519 


860 


1188 


30 


42 


250 


358 


604 


887 


1266 


32 


28 


136 


217 


373 


723 


1009 


34 


42 


173 


269 


448 


775 


1086 


36 




25 


73 


163 


526 


815 


43 


2 


26 


86 


17- 


508 


812 


41 


2 


46 


130 


227 


514 


874 


45 




15 


34 


81 


219 


460 


49 




2 


21 


52 


216 


476 


52 




6 


5 


30 


185 


427 


53 




1 


7 


16 


69 


201 


55 




2 


7 


7 


71 


154 


54 




3 


5 


7 


33 


115 


56 






2 


6 


24 


72 


No. tested 


151 


356 


381 


549 


671 


891 


57 


55 


266 


449 


658 


950 


1317 


58 


86 


295 


479 


742 


1053 


1475 


69 


8 


98 


228 


423 


782 


1145 


60 


19 


134 


341 


599 


942 


1363 


61 


45 


239 


447 


729 


1060 


1556 


62 




21 


54 


73 


253 


478 


63 


78 


266 


483 


786 


1055 


1556 


64 


13 


132 


314 


496 


882 


1388 


65 




19 


44 


109 


315 


582 


66 


7 


93 


266 


488 


751 


1115 


67 


22 


109 


319 


576 


891 


1375 


68 


2 


43 


91 


192 


419 


726 


69 


20 


157 


264 


482 


769 


1173 


70 




20 


72 


130 


385 


674 


71 


5 


74 


195 


391 


683 


1124 


72 


33 


97 


229 


361 


642 


943 


No. tested ^ 


100 


268 


357 


517 


643 


865 



1 Some children did not have a chance to complete the sentences on the last page as their 
attention was not called to the fact that it contained sentences. 



Calculation of the Difficulty of Test Sentences 69 

The remaining lists of tests were treated in the same manner 
as the Graded Series. The corrections to be made for differences 
of ability were derived by examining the behavior of the sentences 
of Language Scale A, which were always given with the new 
sentences in order to obtain just these comparisons. Correc- 
tions for the lack of grade groups were made by finding what 
would have happened if these grade groups had not been used in 
making up from Tables XXIX and XXX the final measure of 
the difficulty of the sentences of Scale A. 

The following tables give merely the score made on each sen- 
tence, the number of pupils tested, and the final position assigned 
to the sentence.^ In those cases where a sentence appeared 
in two different lists and therefore has two estimates of its 
final position recorded in the following tables, it will be well 
in practice to make use of the arithmetic average of the two 
determinations. 

TABLE XLI 

Estimated Final Values of Sentences in Intermediate School Series 

Sent. No. Value 

57 5.98 

58 5.55 

59 7.46 

60 6.83 

61 5.85 

62 8.92 

63 5.54 

64 7.02 

65 8.74 

66 7.40 

67 6.93 

68 8.28 

69 7.16 

70 8.50 

71 7.64 

72 7.55 



^ To show here the individual steps taken with each group of sentences would 
require the printing of an enormous quantity of statistical tables and would 
add nothing to the value of this study. The same methods and the same care 
were employed to secure accurate results as in the case of the sentences of the 
Graded Series. Publication of the scores made on these sentences will make 
it possible for other investigators to use my results in any way that may seem 
desirable. 



70 



Completion-Test Language Scales 



TABLE XLII 

ScoEE Made on Each Sentence of High School Shoet Test 



Sentence 


Grade 


Grade 


Grade 


Grade 


No. 


IX 


X 


XI 


XII 


2 


160 


98 


60 


40 


4 


160 


100 


60 


39 


7 


158 


100 


60 


40 


11 


160 


100 


58 


40 


22 


162 


97 


60 


40 


29 


160 


98 


58 


40 


23 


156 


95 


53 


40 


24 


145 


92 


57 


37 


27 


132 


83 


55 


33 


31 


122 


78 


54 


40 


28 


125 


84 


50 


34 


30 


126 


83 


51 


32 


37 


114 


80 


41 


29 


34 


110 


77 


47 


35 


36 


99 


70 


40 


23 


43 


111 


65 


46 


30 


41 


92 


65 


39 


33 


45 


64 


51 


34 


21 


49 


64 


67 


31 


25 


52 


48 


50 


37 


31 


53 


24 


33 


18 


18 


55 


18 


44 


25 


17 


54 


8 


16 


4 


9 


56 


16 


14 


10 


10 


78 


29 


35 


20 


22 


79 


73 


63 


36 


23 


80 


69 


64 


36 


27 


81 


75 


65 


35 


25 


82 


37 


29 


26 


19 


83 


25 


27 


15 


18 


84 


12 


19 


13 


13 


85 


8 


8 


4 


2 


86 





4 








87 


15 


12 


12 


• 7 


88 


15 


17 


5 


7 


89 


1 


1 


1 





No. tested 


81 


50 


30 


20 







Calculation of the Difficulty of Test Sentences 



71 



TABLE XLIII 
Estimated Final Values of Sentenc- s in High School Short Test 



Sent. No. 
78 
79 
80 
81 
82 
83 
84 
85 
86 
87 
88 



Value 

9.63 

8.91 

8.59 

8.92 

9.76 

10.20 

10.53 

11.58 

12.65 

10.75 

11.14 

12.31 



TABLE XLIV 
Scores Made in High School Half Test 





Sentence 


Grade 


Grade 


Grade 




No. 


X 


XI 


xn 




4 


84 


400 


264 




7 


82 


401 


268 




22 


82 


397 


264 




24 


76 


372 


241 




27 


75 


333 


237 




30 


73 


340 


230 




37 


55 


276 


194 




36 


50 


248 


187 




45 


30 


179 


140 




49 


39 


238 


155 




55 


15 


114 


100 




54 


10 


51 


51 




70 


68 


323 


223 




65 


49 


252 


187 




79 


44 


263 


190 




90 


7 


73 


48 




91 


28 


118 


89 




92 


26 


158 ■ 


104 




93 


27 


179 


125 




94 


51 


210 


182 




95 


46 


264 


211 




78 


12 


68 


77 




82 


37 


165 


136 




83 


12 


37 


45 




84 


7 


52 


36 




96 


16 


70 


66 




97 


10 


42 


38 




No. tested 


42 


204 


136 










72 Completion-Test Language Scales 

TABLE XLV 

Estimated Final Values op Sentences in High School Half Test 

Sent. Value 
No. 

70 7.33 

65 8.03 

79 8.05 

90 10.79 

91 9.88 

92 9.71 

93 9.53 

94 8.15 

95 7.94 

78 10.65 

82 9.37 

83 10.90 

84 11.17 

96 10.48 

97 11.11 



TABLE XLVI 
Scores and Estimates of Final Values for Second Grade East Test 



Sent. 


Value 


Score 


No. 






73 


1.18 


475 


74 


1.28 


436 


75 


1.63 


353 


1 




468 


2 




427 


4 




469 


76 


1.97 


302 


77 


1.09 


429 


3 




308 


5 




276 


6 




324 


8 




138 


10 




172 


7 




115 


11 




75 


29 




54 



Calculation of the Difficulty of Test Sentences 73 

TABLE XLVII 

Scores^ Made on Intermediate Grade Half-Test Sentences 



Sent. 


Grade 


Grade 


No. 


VII 


VIII 


98 


333 


388 


99 


208 


296 


100 


103 


171 


101 


287 


315 


102 


344 


380 


103 


82 


126 


104 


68 


133 


105 


274 


357 


106 


270 


351 


107 


251 


321 


108 


59 


72 


4 


400 


459 


7 


402 


453 


22 


400 


446 


24 


361 


413 


27 


231 


301 


30 


278 


318 


37 


207 


249 


36 


88 


121 


45 


64 


80 


49 


40 


78 


55 


14 


25 


54 


6 


16 


No. tested 


207 


232 



1 The final values of these sentences were not estimated, but the scores are given here in 
order that anyone who wishes to estimate their difficulty may have the necessary data. 



APPENDIX 



APPENDIX 

I. CORRELATIONS 

The writer of this monograph has not as yet undertaken a systematic 
study of the correlations shown by the language scales presented here. Such 
a study needs to be made, however, before it will be possible to say just how 
these tests are related to other tests of knowledge and ability. Such correla- 
tions as are reported here have been worked out incidentally, sometimes as 
a matter of curiosity and sometimes in connection with other studies. They 
are reported here merely to show the need that exists for further investigation. 

Simpson, ^ who made a very thorough investigation of the correlations of 
intellectual tests, including the paragraph completion test, which he calls the 
Ebbinghaus test, has this to say with regard to the reliability of the completion 
test (p. 48) : "Test XIV, Ebbinghaus mutilated test, was very high in reliability 
as used, easily the highest of all. The coefficients of correlation between the 
two halves of the test are: .96 for the Good, .93 for the Poor, and .92 for all 
together. It is beyond question a good test, and should be perfected and 
standardized, with a considerable number of specimens graded in difficulty." 

Simpson estimates (p. 63) the true correlation between the Ebbinghaus test 
and the other tests used in his study as follows: Ebbinghaus test correlates 
with Hard Opposites .85, with Memory of Words .82, with Easy Opposites 
.72, with A Test .54, with Memory of Passages .71, with Adding .65, with 
Geometrical Forms .36, with Learning Pairs .60, with Completing Words .60, 
with Drawing Lengths .15, and with Estimating Lengths .33. His corrected 
coefficient for the correlation between the Ebbinghaus test and Estimated 
Intelligence is .89 (p. 75). 

The Language Scales proposed in this report differ somewhat from the 
paragraphs used by Simpson in his study, and the correlations he has reported 
would probably not apply exactly to the tests used in this study. Although 
the writer is inclined to believe that the sentence tests are more accurate and 
that the correlations with them will be even higher than those shown with 
the paragraph tests, a thorough study of the correlations of the sentence tests 
is the only way in which this belief can be proved or disproved. Such a study 
will undoubtedly be made very soon. In the meantime the following results 
are suggestive of the sort of correlations we may expect. 

In an unpublished study of the mental abilities of dependent children in 
certain institutions,^ the "preliminary list" of completion-test sentences men- 
tioned on page 4 was given, along with the Binet-Simon tests, the Stenquist 



> B. R. Simpson: Correlations of Mental Abilities. Teachers College Contributions to Edu- 
cation, New York, 19 12. 

5 Since the above section was written, this study has been published in the Archives of Psy- 
chology, No. 33, Sept., 1915. J. L. Stenquist, E. L. Thorndike, and M. R. Trabue: The Intel- 
lectual Status of Children who are Public Charges. 

77 



78 Completion-Test Language Scales 

tests of mechanical construction ability, and certain other tests. Before 
sending in the report of the results, the writer worked out a few coefficients 
of correlation ^ with two groups of children. In a group of 50 boys and girls, 
ages 10-16, the completion-test sentences gave a coefficient of .74 with the 
Binet tests, and .46 with the Stenquist test, which showed a coefficient of 
.62 with the Binet test. With a group of 39 boys, ages 10-16, the results were 
as follows: 

Completion tests with Binet tests, r= .85 
Completion tests with Stenquist tests, r= .59 
Stenquist tests with Binet tests, r = . 58 

In a certain seventh grade class of 30 children, in which some of the graduate 
students at Teachers College made a number of tests, Language Scale A made 
coefficients as follows: 

with English Composition (Hillegas Scale), r= .72 
with Courtis Problems in Division, r= .04 

with Thorndike's Reading S :ale Alpha, r= .47 
with Thorndike's Reading Scale A, r= .49 

In the sixth grade of 33 pupils, where the writer gave a number of tests, the 
results were as follows: 

Language Scale A 
with teacher's estimate of intelligence, r= .74 
with Woody Multiplication Test, r= .51 

with Courtis Multiplicati n Test, r= — .12 

with Thorndike's Scale Alpha, r=.47 

In a second sixth grade of 29 pupils, the results of certain tests were combined 
and the correlation worked out between the combined scores and the scores 
in Language Scale A. The results were as follows: 

Language Scale A 

with Combination of all marks made in one semester at school, r= .49 
with Combination of Thorndike's Scale Alpha, Buckingham's 

Spelling Scale, and Hillegas's Composition Scale, r= .58 

with Combination of Vocabulary Test, Opposites Test, 

Mixed Relations Test, and Proverbs Test, ''=•39 

As indicated above, these coefficients are not numerous enough or reliable 
enough to prove anything conclusively. They do suggest, however, that there 
is a positive and rather intimate relation between ability to complete sentences 
and ability in other tests of language and general intelligence. 



'Since there was good evidence that none of the tests used were evenly graded as to difBculty, 
it seemed best to use Spearman's formula, which takes into account only the relative positions 
of the individuals in the different tests. This formula, which is given on page 168 of Thorn- 
dike's Mental and Social Measurements, is as follows: 

fl= T — ■ The p values are then converted into r values by means of the table given 

'^ m(w2-I) 

by Thorndike, which shows the r value for each possible p value as derived from the formula 



<?0- 



Appendix 79 

One rather surprising correlation has been reported to me by Professor W. D. 
Scott, of Northwestern University. Thirty efficiency experts employed by 
a large industrial concern in New England were tested by Dr. Scott, who used 
ten different tests, including a list of completion-test sentences prepared by 
the writer. Each member of the firm who knew the thirty experts made a list 
of them, arranging them in order according to his judgment of their efficiency 
as efficiency experts. Professor Scott mailed a list of the men, ranked according 
to the results of his ten tests, and on the same day the members of the firm 
mailed their lists to him. Professor Scott's combined results gave a coefficient 
of .87 with the combined judgment of the employers. The completion test, 
which was only one of the ten tests, had a coefficient of .64 with the employers' 
combined judgments, and with the combined result of all ten tests, r = .6g. 



2. SCHEME FOR SCORING SENTENCES 

The question of what should be called correct and what should be called 
incorrect in scoring the sentences as completed is a question upon which a great 
deal of time and worry may be spent. The important thing about scoring 
the sentences, however, is not that the scheme used shall be absolutely per- 
fect, but that the scheme used shall be used consistently. 

These sentences might be used to measure a great variety of qualities in 
the individual completing them. For example, we might score altogether 
according to the correctness of the grammatical forms used. On the other hand, 
we might ignore grammar altogether and make these sentences test the child's 
understanding, scoring according to the child's grasp of the ideas suggested 
by the printed words. We might score according to the judgment shown 
or the truthfulness of the child's statements in the sentences as completed. 
Again, it might be possible to use these sentences as tests of memory for 
phrases, of richness of associations, of unity and clearness of expression, of 
aptness in the choice of words, of imagination, or of other characteristics. 

The scheme that has actually been used has not been any particular one of 
the above possibilities, but simply a general combination of all of them. In 
some cases one element may have predominated in causing a decision, and 
in other cases another element. No one needs to follow the scheme shown 
below if he finds it wrong, for it is only given in order that it may be perfectly 
clear just which combinations were allowed and which were not allowed in 
this study. The important things for one to do are to be sure that he is 
making no great errors in judgment, to be consistent, and to report just how 
he did score each sentence. The writer suggests that the detailed scheme 
shown on the following pages be used as it stands in so far as possible, in order 
to secure uniformity and comparability .^ 



iWith the preliminary series, s points were given for perifect, 4 for slightly less than perfect, 
3 for still less, etc. The present scheme (2-1-0) is practically the same as though the lower end 
of the older scheme (s-4-3-2-1-0) had been omitted, using 2 in place of 5, i in place of 4, and 
o in place of 3, 2, i and o. With 40 pupils in each grade, the correlation between the relative 
difficulty of the preliminary -list sentences in the 6A grade and their relative difficulty in the 8B 
grade was .965 by the s-o method, .962 by the 2-0 method now used, and .958 if everything 
now scored 2 and i were called " right," and everything else " wrong." 



8o Completion-Test Language Scales 

The following general scheme has been the basis upon which the more detailed 
judgments have been based: 

General Scheme 

Score 2 

A score of 2 points is to be given each sentence completed perfectly. Errors 
in spelling, capitalization, and punctuation should not be allowed to affect the 
score. 

Score I 

A score of i is to be given each sentence completed with only a slight im- 
perfection. A poorly chosen word or a common grammatical error, which 
makes the sentence less than perfect and yet leaves it with reasonably good 
sense, should serve to reduce the score from 2 to i. 

Score o 

A score of o is to be given if the sentence as completed has its sense or con- 
struction badly distorted. A sentence must have reasonably good meaning 
and express a sentiment which might honestly be held by an intelligent person 
in order to receive a higher credit than zero. 



Detailed Scheme 

In those sentences having only one blank to be filled, any word appearing 
under the heading Score 2 was considered entirely satisfactory as a completion 
of the sentence. Those words appearing under the heading Score 1 were 
given half credit — a score of I — while the words appearing under Score were 
given a score of o. The score of each sentence should be written on the test 
paper just under or at the end of the sentence. 

In those sentences where more than one blank appears, the different groups 
of words appearing below are arranged in their proper order and are connected 
by a dotted line to show the proper sequences: the first group on the left 
hand side of the page being words for the first blank in the sentence, and the 
dotted line showing what words are used in the next blanks to make up a 
combination of the value shown by the heading Score 2, Score i, or Score o, as 
the case may be. The commas are used merely to separate the fillers for 
the same blank and are not a part of the completion. An asterisk following 
a bracketed group of words indicates that this group of words will be indi- 
cated thereafter by an asterisk alone. Double asterisks, triple asterisks, etc., 
are also used to refer to and stand for entire groups of words. This device 
obviates the necessity of repeating an entire list of words for each combin- 
ation in which the list may be used. 

The lists given in the following pages are not exhaustive, but they are 
suggestive of the way the scoring has been done. In many cases a different 
tense of the same word has not been recorded. Anyone who uses this scheme 
will be called on constantly to make judgments upon new combinations. 



LANGUAGE SCALE B 

I . We like good boys girls. 

Score 2 

and, an, und, 
Score I 

or, not, and good, also, 
Score o 

for, with, said the, and the, 

6. The is barking at the cat. 

Score 2 

dog, hound, 
Score I 

dogs, boy, dog. 
Score 

man, cat, god, 

8. The stars and the will shine tonight. 

Score 2 

moon, 
Score I 

light, planets, lights, 
Score o 

dipper, stripes, clouds, city, sky, sun, 

22. Time often more valuable money. 

Score 2 

is, was than. 

Score I 

seems, becomes, .... than, 
Score o 

are with, is with, 

23. The poor baby as if it were sick. 

Score 2 

cries, cried, acts, acted, 1 ^ f very, getting, 

lies, lay, looks, looked, J • • • ■ | quite, extremely, 
Score I 

suffers, suffered, appears, moans, sighs, 
lays, feels, behaves, was crying, groans, 
acts, looks, plays, .... never, 

f feeling, nearly, dangerously, rather, almost, 
*. . . . \ real, awfully, terribly, pretty, half, home, 
[ sea, bad, about, often, so. 
Score o 

* . . . . not, was .... very, 

81 



82 



Completion-Test Language Scales 



31. She if she will. 

Score 2 

can, may, 
Score I 

will, may go, can do well. 
Score o 

does, works, goes, has, is, could, knows, might, plays, is good, can't, 

35. Brothers and sisters always to help 

other and should quarrel. 

Score 2 

(try, strive, offer, seek, | 
agree, endeavor, learn, aim, f * • • each . 
attempt, want, J 



not 
never. 



Score I 

must . 

should 



should 
nearly 
ought . 
most . . 
Score o 
should 
can . . . 
are . . . 
have . . 
are . . . 



. . . each .... **, 
consent, like, go, work, love, 
be ready, come, have, wish, 
expected, able, supposed, told, 
glad, happy, willing, eager, ready, 
bade, careful, good, apt, trying, 
together, best, needed, 
... * .... the, an, one, one an, . . . . 
. . . haV^e .... each ....**, 
. . to try .... each ....**, 
..*.... each ....**, 

... * .... out, along, some, ....**, 
go .... one ....**, 
ready .... one ....**, 
. . had .... each ....**, 
kind .... each ....**, 



.each. 



.each. 



* . . . . has . . 



38. ^ weather usually a good effect 

one's spirits. 

Score 2 

Cold, Pleasant, Balmy, Frosty, 

Winter, Bright, Clear, Moderate, 

Brisk, Spring, Fair, Cool, Mild, 

Warm, Autumn, Beautiful, 
Score I 

*.... had ....**, 

Summer, Good, Fine, Nice, The, Hot, Sunny, 

Calm, Rainy, Temperate, This, Such, Damp, 

Windy, 

* . . . . takes, produces, ....**, 

Summer, Good, .... has ....**, 



on, 
upon. 



has 



. ** 



Score o 

*, Summer, Damp, Bad, 

* . . . . makes, shows, . . . 

* . . . . gives .... to. 
Bad has **. 



A'p'pendix 

has, is, .... to, in, 



83 



48. It is very annoying to toothache, ... . 

often comes at the most time imaginable. 

Score 2 



have. . . (a, the,) * . . . which . 



suffer .... from, with, .... 
Score I 

get, feel, suffer, bear, ....*. 



trying, unexpected, absurd, 
inconvenient, embarrassing, 
annoying, unwelcome, unusual, 
distressing, extraordinary, 
disagreeable, inopportune, 
undesirable, unfortunate, 
unsuitable, unreasonable, 
objectionable, 
hich ....**. 



have ....*, 
suffer. . . .from. 



. which ....**, 

horrid, awkward, terrible, crit- 
ical, unpleasant, busy, strange, 
important, unthinkable, pe- 
. which.... { culiar, unlucky, harmful, val- 
uable, strange, unlikely, un- 
satisfactory, unprepared, un- 
certain, awful, queer, 
have. ...*... .for it, as it, and it, that, it, . . . .**, 
Score o 

have. ...*... .and. ...**, 

, ^ ... J unknown, pleasant, happy, 



\ joyful, worst, sudden, 
1 the 

worth . . . . \ time, effort, trouble, [ *• 



54. To friends is always the it takes 

Score 2 

have, make, win, 

gain, be, help, keep, 
Score I 

see, satisfy, meet, greet, know, please, find, 1 , ^^ 

treat, visit, entertain, possess, obtain, j ■ ■ ■ ■ • • • • 1 

* . . . . worth .... endeavor, energy, pains, patience, work, 
Score o 

* . . . . for, worthy of, ... . **, 

win .... better .... longer, 

our .... given . . . .best. 



LANGUAGE SCALE C 



2. The sky blue. 

Score 2 

is, was, became, turned, looks, appears, seems. 
Score I 

got, is very, is not, is, as, has. 
Score o 

are, light, very, dark, 

5. Men older than boys. 

Score 2 

are, act, look, appear, seem, 
Score I 

grow, were, 
Score 

be, see, 

12. Good boys kind their sisters. 

Score 2 

are .... to. 
Score I 

were, must be, should be, will be, act, is, .... to, 

are .... with, toward, like, also, and, 

and .... love, think .... of, do ... . things for, 

say .... words to. 
Score o 

are .... for, as, by, 

19. The girl fell and her head. 

Score 2 

hurt, injured, bruised, cut, hit, struck. 
Score I 

bumped, knocked, came down on, cru^lied, fractured, broke, 
Score o 

split, busted, on, bunked, 

24. The rises the morning and ..: at 

night. 

Score 2 

sun .... in, during, .... sets, sinks, disappears. 
Score I 

temperature .... in .... falls, 

boy, bird, .... in .... sleeps, rests, 
84 



Appendix 



85 



tide 



also, falls, 

I falls, goes, leaves, lowers, sits, moon, never, 
goes down, set, not, descends, drops, dies, 
the moon, fades. 



Score 






sun . . 


. . in ... 


sometimes, 


sun . . 


. . every 


. . . . sets, 



30. The boy who hard do well. 

Score 2 

works, tries, studies, thinks, .... will. 
Score I 

tries .... can, may, does, shall, should, could, must, 

worked, tried, .... did, will, can, 

plays, hits, work, .... will. 
Score o 

tries .... sometimes, surely, often, 

did .... work did, does .... work, work .... did. 



37. Men ..., more 

women. 
Score 2 



to do heavy work 



have 
Score I 



able, competent, willing, 
inclined, apt, ready, likely, 
ability, strength, inclination, power, .... than, 



than. 



prepared, anxious, eager, liable, fitted, 
equal, accustomed, suited, satisfied, fit, 
capable, used, adapted, wanted, re- |- .... than, 
quired, taken, healthy, qualified, built, 
stronger, suitable, useful, 
ambition, energy, time, 
muscle, tools, right, business, 
try, like, ought, .... often .... than, 
earn .... money .... than, has .... ability .... than, 
. how .... than, eat .... food .... than, 
. tools, money,. . . . than, appear ....*.... than. 



have 



than 



know 
need 
Score o 
are . . 
are . . 
do .. 



. made, asked, good, active, .... than, 
. useful, able, .... for, work .... hard .... than, 
thinking .... than, have .... brains, work .... than, 

44. The sun is so that one can not 

- directly causing great discomfort to the 

eyes. 
Score 2 

brilliant, dazzling, \ ^, f look, gaze, 1 ** . . , 

J. ^u-u^(----\^ >**.. .at. . .It. . .without, 

radiant, bright, I I stare, J 



86 



Completion-Test Language Scales 



. .at. . .it. . .without, 



Score I 

blinding, intense, strong, light, 

powerful, glary, hot, red, fiery, high, 

*. . . . endure, bear, stand, .... its .... rays .... without, 

*....**.... into, toward, towards, .... it .... without, 

*, blinding, intense, ....**.... at .... it ... . unless, for, if, 

low .... read .... a ... . book .... without, 

*. . . . even .... look .... up .... without. 
Score 

warm, far, low, ....**.... at .... it .... without, 

*....**.... at .... it .... because, thus, 

*. . . . see .... it .... so .... without, 

53. The knowledge of use fire is of 

important things known by but unknown 

animals. 

Score 2 

the, many, \ ^ \ man, men, us, 1 ** 
several, J \ mankind, people, J 

to, by, \ ^^^ 
among, J ' 
Score I 

how .... to ... . one ....*.... persons, scouts, humans, .... ***, 
why .... we .... one ....*....**.... ***, 
when, having, the way, .... to .... one ....*....**.... ***, 
how .... to ... . considered, rated, thought, ....*....**.... ***, 
how .... to .... one .... most ....**.... ***, 
Score 

how .... to .... often ....*....**.... ***, 
proper, correct, careful, 
important, skillful, great, 
knowing .... how to .... one .... 



how . . . . to . . . one . . 



the. . 



. . . one . . . 

4c4c *** 



** *** 



56. One ought to grteat care to 

of , for one who 

it to get away from them. 

Score 2 

form, choose. 



.. the right 
bad habits 



use, take, 
exercise 



:e, 1 
' J 



acquire, gam, 

cultivate, 

develop, adopt, \ 

establish, 

learn, teach, 

begin, 
has, gains, contracts, ] 
forms, acquires, [ *^ 

contracts, J 



sort, 
kind. 



. habits 



f hard, [ *.),:), 
.finds. . . . \ difficult. 



habits . . < 



Score I 



Appendix 

living, life, 
working, work, 
studying, study, 
speaking, speech, 
thinking, thought, 
learning, mind, 
procedure, action, 
attention, acting. 



87 



*** ■ • • * 



. . . finds . . . ' 



obtain, get, 
possess, use, I 
have, pursue 
make, lead. 



. habits . 



***. . . .habits 

*** 

habits .... *** 




have, 
give, 

take. 



***. . . .habits 
habits .... *** 



habits. . . .*** 



.finds. 

has, 
makes, 

. . finds . 



***.. finds..***, 
/ impossible. 



pays. 



*** 



[ ***.... habits j 

*** .... speech .... *** . 



** ' 



be .... *** 

** habits 

begin 

do .... thing .... course . . . . 

do .... ***.... things ....*** 



person . . . . ^, 

\ morality, 
I manhood, 
. . way .... living .... *** . 



** » 



Score o 



/get 
\do , 



, start .... life 
thing .... life 



. . . finds 

finds . . 

. *** .... finds 
* 

, . . finds 

. . . finds 

finds ....***, 

.... finds....*** 



** ' 



*** 



LANGUAGE SCALE D 

4. We are going school. 

Score 2 

to, through, toward, before, after, 
Score I 

into, from, to the, as a. 
Score 

at, in, 

76. I - to school each day. 

Score 2 

go, come, 
Score I 

am, am going, like to go. 
Score o 

like, to, going, 

II. The plays her dolls all day. 

Score 2 

girl, child, baby, .... with. 
Score I 

boy, girls, cat, dog, children, little girl, .... with. 
Score o 

girl .... to, for, 

21. The rude child does not many friends. 

Score 2 

have, make, gain, win. 
Score I 

deserve, find, know, acquire, possess, keep, greet, appreciate, 

accumulate, help, please, obey, meet, get, see, 
Score o 

want, like, care for, need, has, 

63. Hard makes tired. 

Score 2 

one, people, you, him, her. 



work . . . . ^ . 

me, men, women, them, us, 

Score I 

work .... a man, minds, bodies, 
traveling, tasks, luck, things, ....*, 

Score o 

thing, bread, times, ....*, 



Appendix 89 

27. It is good to hear voice friend. 

Score 2 

, , fa, one's, our, your, my, another, 

\ some, his, her, any, their, 

Score I 

the .... of .... one, an old, a true, the, an intimate, 

your .... my .... dear, good, her .... to ... . her, 

a . . . . from, of, .... a, your, her, .... calling .... your, her, 

your .... again, tonight, .... my, that .... of ... . my, 

Caruso's .... with .... his, her .... said .... Mary's, 

Score 

the .... from ....*, your .... with, than, .... your, 
one's .... said .... his, a .... of, from, .... your, 
his ... . and .... his, 

71. The happiest and contented man is the one 

lives a busy and useful 

Score 2 

(most, best,)* (who, that,)** life. 

Score I 

* . . . . which .... life, 

well, brightest, richest, the, nice, 1 ^^ ... 

loveliest, strongest, healthiest, more, J ' 

Score o 

good, poor, ....**.... life, 

42. The best advice usually obtained ^ 

one's parents. 

Score 2 

(may, can, will,)*. ... be ... . from, 

(directly, that, correctly, freely, l ^^ 
easily, readily, promptly, first, > , 

fully, soon, accurately, properly, J • • ■ • > 

has, .... been .... from. 
Score I 

might, could, would, should, .... be .... from, 
*. . . . be .... of, by, through, 

(rightly, well, best, only, ] 
to be, better, willingly, > . . . . from, 
fairly, cheerfully, J 

is ....**.... of, by, through, most, received, .... is ... . from, 
one .... has .... from, comes .... when .... from. 
Score o 

is .... always, often, not, also, being, .... from, 

children .... have .... from, is ... . best, to be, .... by. 



9Q 



Completion-Test Language Scales 



51 things are satisfying to an ordinary- 

than congenial friends. 

man, person, child, mortal, 
individual, boy, girl, woman. 



Score 2 




Few . . 


. . more 


Most . 


. . less 


Score I 




Few . . 


. more 


Play . . 


. . more 



friend, companion, stranger, 

people, acquaintance, 
child, boy, girl. 
Many, Some, No, Good, Sometimes, | 

These, More, Those, New, One's f . . . . more, less, ....*, 

Queer, Such, Many, Ordinary, What, J 
Score o 

Kind, All, The, Small, Often, Flattering, .... more ....*, 
Few .... more .... one, condition. 
Few .... not .... man, Many. . . . more . . . .friend, 
Many .... quite ....*, 

84 a rule one association friends. 

Score 2 

, (enjoys, prefers, likes, desires, welcomes, seeks,)*. . . .with. 



As 
Score I 

As 

As 

Score 

As 
As 



... of. As ... . makes .... with, 
holds, keeps, cultivates, 
chooses, wishes, loves, 

chooses .... and, 
keeps .... his. 



;es, finds, 1 
3, gains, J 



with, of, 



Although 



like 



of, 



LANGUAGE SCALE E 

73. I see you. Can you see ? 

Score 2 

me, 
Score I 

the cat, men, us, it, 
Score o 

I can, yes, 

75. Ice is cold, but fire is 

Score 2 

hot, warm. 
Score I 

good, not, red, burning, 
Score o 

how, burned, cold, 

7. The kind lady the poor man a dollar. 

Score 2 

gave, gives, oflfers, offered, paid, pays, took, sent, loaned, lent, 

handed, tendered, 
Score I 

found, lends, loans, hands, sends, takes, give, is giving, 
Score 

finds, helps, owes, owed, 

18. The best to sleep is at night. 

Score 2 

time, 
Score I 

hour, way. 
Score o 

place, bed, air, girl, boy, of all, go, thing, when, thing is, 

58. Children should many lessons from 

parents. 

Score 2 

(learn, take, receive, obtain, get,)*. . . . their. 
Score I 

study, have, observe, know, .... their, 

obey .... from, 

*.... the. 
Score 

show, do, recite, .... from, have .... your, 

91 



92 Completion-Test Language Scales 

25. The child the river was drowned. 

Score 2 

fell. . . .in, into, .... and, 

went, sprang, \ . ^ , 

J J J } ■ ■ ■ ■ into .... and, 
jumped, waded, J 

Score I 

swam, bathed, played, was, .... in ... .and, 

f to, down, on, \ , 

went . . . . < . > . . . . and, 

[ near, m, J 

ran .... to, into, .... and, played, sat, .... near .... and, 

who .... crossed .... yesterday, who fell .... into .... soon, 

C , ., was ... .at, on, . . . .and, 

playing ....< u I. pl^^yi^g .... near .... accidentally, 

Score 

went .... by .... and, was .... to, by, .... and, 

played .... at .... and, goes .... to .... and, 

swam .... through .... and, playing .... by ... . today, nearly, 

34. It is a task to be kind to every beggar 

for money. 

Score 2 

hard, burdensome, | 

difficult, great, big, \ *■ ■ ■ (who, that,)**. . . (asks, begs, pleads,)*** 

real, trying, j 

Score I 

philanthropic, charitable, heavy, ] 

bitter, noble, small, foolish, pleasant, > ....**.... ***, 

good, little, bad, kind, worthy, mean, j 

*....**.... calls, cries, comes, seeks, wants, looks, wishes, works, 

* . . . . when .... asked, he asks, * . . . . asking .... one, 

* . . . . which .... ***, 

Score o 

daily, poor, fine, nice, friendly, easy, ....**.... ***, 

* . . . . which .... calls, cries, comes, etc. *....**.... needs, 

polite .... here .... asking, good .... that .... comes, 

36. Worry never improved a situation but has 

made conditions 

Score 2 

(often, usually, always, generally, merely, 1 
undoubtedly, sometimes, only, certainly, f * • • worse, 
slowly, probably, simply, repeatedly surely, J 
certainly, surely, ....*.... worse. 



Appendix 



93 



Score I 

, J rather, really, ever, mostly, even, 

' " ' ' \ instead, just, indeed, helped, c ■ ■ • • > 

has ....*.... serious, poor, change, poorer, bad, harder, miserable, 
has .... always, gradually, .... serious, poor, etc. 

Score o 

has .... never .... worse, will .... often .... worse, 

has .... never, often, .... better, should .... often .... worse, 

never .... often .... worse, can .... sometimes .... worse, 

52. When one feels drowsy and , it happens 

that he is to fix his attention very successfully 

anything. 



Score 2 

dull, tired, stupid, weary, 
fatigued, lazy, indolent, 
sleepy, inattentive, ill, 
inert, indisposed, sick, 



*. . . . (seldom, rarely, never,)***. 
Score I 

' weak, sad, bored, cross, is, tired, . 
*. . . .***. . . .able. . . .to, at. 



usually, always, 

generally, 

frequently, 

sometimes, often, 

on, \ 
upon, J 
able .... ***, 



. unable 



" . . . . unable 1 
'=*.... able \ 

1 



. invariably, soon, just, then, so, .... unable. . . .***, 

,**... .failing, able, slow, unfit, not able, too tired, unfit, . . *** 

.*** trying, going, ready, liable, apt, . . . .***, 



lazy 
Score o 



apt .... on. 



. never . 



sick .... generally .... made .... ***, 



sleepy .... often .... not .... ***, 
tired .... sometimes .... lazy .... on, 

83. In order clearly at .... 

to artificial 

Score 2 



It is 



to . . . see . . night . . . necessary . 

Score I 

times, 
all, sea, 



use. . . . (light, means, devices,)* 
have .... light. 



to. 



necessary, 
essential. 



. . have, use . 



to. . .think. . . < .. ' >.. .necessary. .. < '., ? ..stimulants. 



94 Completion-Test Language Scales 

to .... look .... light .... necessary .... have .... protection, 
to .... see .... night .... better, best, .... use ....*, 

to .... hear, speak, .... times, first necessary .... use, 

adopt, .... means, 
to .... understand, explain, .... times, .... necessary .... use 

.... examples, 
to .... see .... night .... necessary .... use .... glasses, 
Score o 

to .... see .... distance .... better .... have .... light, 

to .... see .... once .... best .... try .... means, 

to ... . look .... something .... advisable .... remove .... aids, 

to ... . think .... times .... necessary .... use .... means, 



LANGUAGE SCALE J 

29. Boys and soon become and women. 

Score 2 

girls .... men, 
Score I 

girls, girl .... man, girls .... gentlemen, 
Score o 

girl .... mans, men .... poor, 

61. The are often more contented the rich. 

Score 2 

poor .... than. 
Score I 

poor, people, .... with, by, children, people, .... than, 
girls .... with. 
Score o 

girls, men, parents, .... than, 

64. The rose is a favorite because of fragrance 

and 

Score 2 

flower .... its .... beauty, color. 
Score I 

flower .... the .... beauty, color, smell, blossoms, sweetness, 

flower .... its ... . scent, smell, appearance, sweetness, blossoms, 
Score o 

flower .... sweet, nice, .... looks, pretty, 

41. It is very to become acquainted 

persons who timid. 

Score 2 

(hard, difficult,)*. . . . ( :^^!^' thoroughly, fully, | ,, ^.^^ 
\ mtimately, personally, J 
Score I 

trying, tiresome, pleasant, possible, nice, ] 

unusual, awkward, unpleasant, annoying, I 

fine, strange, uncommon, inconvenient, }■**.. .with. . .are, 

kind, easy, grand, good, sensible, 

troublesome, necessary, commendable, 

(really, slightly, merely, closely, properly, 1 
rapidly, fairly, nicely, quite, familiarly, \ . . with . . are, 
readily, quickly, better, much, more, so, J 
*....**.... with .... seem, act, appear, look, 

95 



96 Completion-Test Language Scales 

Score 

nice .... much .... with .... are, 

well, unwise, customary, wrong, bad, ....**... .with .... are, 
* [ good, goodly, kindly, easily, 1 ^.^^^ ^^^ 

' ' ' " \ strongly, real, immediately, J ' 

93. Extremely old sometimes almost as 

care as 

Score 2 

. 1 f need, 1 f babies, 1 

>*....■{ take, I **...much... \ infants, young, \ *** 
' [ require, J [ children, invalids, J 

Score I 

* . . . . are .... much, great, .... ***, 
age .... brings .... much .... youth, 

age .... seems .... much sickness, 

men .... take .... much .... women, 
books .... need .... much .... new, 
people .... have, show .... little .... young, 

Score o 

things ....**.... much .... trouble, 

87. One's in life upon so factors 

it is not to state any single for 

failure. 

Score 2 



j depends, 
\ rests, 



easy. 



success ....■{ _^J^^ ' }*.... many .... that . . . . -j safe, 

wise, J 

rule. . . .avoiding, 

his, her, one's, 

every, any, a, 

Score I 

position, conduct, | ^ ^, ^ 

....*.... many .... that 
course, status, } ** 1 -j- 

. ....**... .rule. .. .avoidmg, 

purpose, aim, j 

f reason, 1 

success. ...*... .many. . . .that. ...**.... \ conditon, \ 

[ factor, J 

one's 

our, complete, 

Score o 

success ....*.... many .... that .... true .... reason . . . our. 



Appendix 97 

89. The future of the stars and the facts of 

history are now once for all, I like them 

not. 

Score 2 

course, destiny, \ ^ J ancient, 



, , . . . . , , . , ** . . fixed . . whether ... or, 

circuits, paths, J \ past, their, 

Score I 

*....**.... known, learned, settled, .... whether .... or, 

* . . . . future .... fixed .... whether .... or, 
Score 

*....**.... fixed, known, .... and, although, .... them. 



LANGUAGE SCALE K 

1 6. The boy will his hand if plays with fire. 

Score 2 

burn .... he, 
Score I 

injure, hurt, heat, warm, ruin, dirty, .... he. 
Score 

use, shake, hold, lose, suck, wash, .... he, 

57. Hot weather comes in the and weather 

the winter. , 

Score 2 

summer .... (cold, snowy, icy,)*. ... in, 

summer .... cool .... precedes, 
Score I 

summer, spring, .... the, bad, rainy, .... in, 

spring ....*... in, brings. 
Score o 

summer ....*.... comes, 

28. The poor little has nothing to ; 

he is hungry. 
Score 2 

Si^child!""' } *• • • (^^^' ^°"'^'^' absolutely.)**. . . .eat, 

Score I 

*. . . . got, received, almost, really, simply, even, probably. . . .eat, 
baby, creature, man, beggar, thing, pig, dog, bird, ....**... .eat, 
*. . . .eaten. . . .day, *,baby, creature, etc eat, 

Score 

*....**... .do, wear. *....( '^°' ^°^' ^^.''^^ ] ... .eat, 

(^ never, entirely, J 

33. Very few people how to spend time and 

to the best advantage. 
Score 2 

(know, learn,)*. . . . (money, energy, effort,)** 
Score I 

* . . . . thought, study, work, think, put it, knows ....**, 
find, show, ....**, 
Score o 

find .... work, think, * . . . . go, send, try, do, 
98 



Appendix 99 

82. One not, as a , attention 

uninteresting things. 

Score 2 

(can, does, will,)*. . . .rule, fact, .... (give, pay,)**. . . .to, 
*,shouId, . . . . rule. ...**... .to, *. . . .child. ...**... .to, 
*. . . .rule. . . .attract, call, direct, ... .to, 
Score I 

*. . . .rule,. ...**, fix, put, hold,. . . .on, 

{student, teacher, \ 1^^ . . . . , 
( to, 

necessity, > . . . . -^ . . . , 

J • maintain .... with, 

reader, practice, , , , , 

' \ hold .... by, 

^ has .... rule .... much .... for, 

should .... idiot, practice, ....**.... to. 

Score o 

* . . . . spectator .... keep .... to, 

looks .... tarter .... giving .... to, 

90. To eat one is is a pleasure. 

Score 2 

(when, whenever,)*. . . . hungry .... (great, real,)** 
(till, until,)*** satisfied **, 

Score I 

*. . . . well, happy, ....**, food, what, .... fond of . . . . **, 
***. . . .full, stuffed, ....**, heartily. . . .told, convinced, ....**, 
what, whatever, .... forbidden, given, .... doubtful, **, 

Score 

delicious .... sure. ...**, when .... enjoying .... marked, 

86 they us not, nature's 

are and unchangeable. 

Score 2 

(suit, affect, 1 f 1 1 

impress, concern, j- *. . .or. . . < ' > **. . .fixed, 

favor, disturb, J { y < ) 

Score I 

Whether .... convince, effect, .... or ....**.... fixed. 
If ....*.... or ....**... . fixed, 

Whether .... influence .... or ....**... .true, inflexible, 
Score o 

Even .... suit .... or ... .roads .... sure, 



LANGUAGE SCALE L 

60. Children are rude not easily win friends. 

Score 2 

(who, that,)* (do, can, will,)** 

Score I 

*. . . . may, should, must, which ,...**, 
Score o 

may be .... but, 

66. Plenty exercise and air healthy 

and girls. 

Score 2 

of .... (fresh, pure, good,)*. . . . makes . . . .boys. 

Score I 

of ....*.... make .... boys, 
of .... clear, plenty of, .... makes .... boys, 
outdoor, work, study, ....*.... makes .... boys, 
of ....*.... is .... to boys, for boys, 

Score 

of .... healthy .... give .... boys, 

70. In to maintain health, one should have 

nourishing 

Score 2 

order .... (one's, his, good,)*. . . . (food, foods,)** 
Score I 

seeking, trying, helping, traveling, 

summer, winter, spring, truth, 

order .... our, your, . . 
Score 

life ....*....**, time ....*. 



eling, 1 

1, illness, J 



\** 



65 happiness can not be with money. 

Score 2 

True, Real, Great, Your, Our, \ ^ ,, , , ^^ 

His, Her, One's, Children's, / " " " ' (*^°"S^^' ^^"^P^'^^'^ 

Score I 

Some, Plenty, No, People's, 1 f **, gotten, secured. 

Often, All, Much, J \ obtained, 

*, Much, Always, Sometiires. . . . . | S°"""' '"""f ^' Y' 

[ won, msured, made. 

Score o 

Good .... made. Your .... counted. Their .... repaid, 

100 



Appendix loi 

32, One's do always express his thoughts. 

Score 2 

(words, statements,)*. . . . not. 
Score I 

expressions, looks, actions, sayings, features, word, lips, .... not^ 

words .... almost, actions .... nearly, most. 
Score o 

ways, eyes, opinions, .... not, expressions .... nearly, 

92. To to wait, after having to go , 

very annoying. 

Score 2 

{prepared, planned, 1 r 1 ^ 

, r J , . , Kfc J somewhere, out, I ^^ . 

decided, promised, >■*....< , > **. .is, 

, , . , 1 away, home, J 

arranged, hurried, J \. ■" ' j 

have ....*.... promptly .... is, have .... asked ...**... is. 
Score I 

have .... waited ....**.... is, 

stop .... attempted ....** .... is, 

have. . . .*, wanted, wished, had,. . . .is. . . .sometimes, often, 

have. . . .lunch. . . .swimming. . . .is, 

have .... had .... quickly, far, .... is, 

have .... somewhere, far, .... often, have .... had . . . away . . . is. 
Score o 

have .... preparing .... there .... is, 

have .... had .... work .... is, 

78. It is sometimes to between two 

of action. 
Score 2 

(difficult, hard,)*. . . .choose. . . . (lines, modes, courses,)** 

necessary .... hesitate ....**, 
Score I 

*, necessary choose, distinguish, .... kinds, types, 

dangerous .... go .... men. 
Score o 

safe .... go .... guns, 

97. One can do his at one while 

of another. 

Score 2 

not, U r best, U,_ r thing, task, job 1 ,,, .thinking, 
never, J ^ duty, J |^ occupation, study, J 

Score I 

*....**.... time, place, .... thinking, dreaming, 
often. ...**.... ***, time, place, .... thinking. 

Score o 

also ....**.... time .... not, *....**.... time .... seeing, 
easily .... work .... time .... talking, 



LANGUAGE SCALE M 

67. One can not foretell will happen in the 

Score 2 

, f future, morning, autumn, winter, 

what '{ ■ U4. A 

\ night, end, sprmg, summer. 

Score I 

city, crowd, present, family, house, 



month, year, morrow, day, world, 
things that ....*, 
Score 

what .... time, past, today, that ....*, 

59. The dog a useful because his 

intelligence and faithfulness. 

Score 2 

is. . . . (animal, creature, friend, pet, beast, companion,)*. . . .of, 
Score I 

is .... fellow, thing, being, dog, .... of, 

becomes ....*.... of , is ....*.... he has. 
Score 

is ....*.... by, has .... manner .... of, 

95. Many people their health because do not 

the of hygiene. 

Score 2 

lose, injure, ruin, 1'^ , f observe, heed, understand, 1 

undermine, destroy, J ' \ know,practice, follow, keep, f *** 

principles, 1 innti 
laws, rules, J * 
keep .... they .... neglect .... *** 

*. . . . they .... know .... need, good, value, meaning. 
Score I 

wreck, mar, haven't, spoil, waste,. . . .they. . . .***. . . .*** 

4 ^1 ^ J J science, subjects, books, 

* . . . . they study < , , 

(^ lessons, study, rules, 

have .... they .... disregard .... study, subject, science. 

Score o 

protect .... they .... want .... disease, 

lose .... they .... acquire .... value, 

have .... they .... follow .... ***, ethics, 

102 



Appendix 103 

79. Nothing can one's happiness effectively 

than a guilty 

Score 2 

destroy, injure, mar, lessen, 1 

J . ., > .... more. ... conscience, 

decrease, rum, spoil, J 

Score I 

harm, hurt, hinder, dampen, eflfect, darken,. . .more. . .conscience. 
Score o 

stunt, hinder, .... more .... man, person, 

45. To many things ever finishing any of 

them a _ habit. 

Score 2 

begin, undertake, 
attempt, leave, 
commence, start, 
try, plan. 

Score I 

take, have, do, make, say, 1 . , ^ ^^ , . 

... .,>.... without ....**.... bad, 

stop, think, get, avoid, J 

*. . . .hardly, before, not, n, never **. . . .bad, 

*. . . .without. ...**.... deplorable, pernicious, tenacious, strange, 

*. . . .without. . . .forms, seems, starts,. . . .bad, 

Score o 

take, have, do, make,. . . .before, not,. ...**... .bad, 

take, have, etc without. . . .seems, starts, forms,. . . .bad, 

do. . . .when. ...**... .bad, *. . . .and. ...**... .bad, 

91. The seems and dreary a dis- 
couraged 

Score 2 

{ man, woman, 

(world, day,)*. . .(dull, dark, sad,)**. . .to. . . 



> * without { t^' ^**..bad, 

' becomes, ' 



person, 
child, 
boy, girl. 



road .... long .... to ... . traveler. 

Score I 

way, time, road,. . . .long. . . .to. . . . ***, voyager, 

teacher, man, boy,. . . .sad. . . .and, over,. . . .***, mortal, 

man .... tired .... after .... attempt, *....**.... when .... ***, 

*....**... .for. . . .***, *....**... .giving. . . .feeling, 

Score o 

*. . . .long. . . .although. . . .***, 



104 

55. 



Completion-Test Language Scales 

that are to one by an 

friend should be pardoned readily than injuries 

done by one is not angry. 

Score 2 



Injuries . . . .done. 



Score I 

Injuries 
Injuries 
Injuries 



Injuries. . .done 



angry, 
angered, 
irate, 
enraged, 



. more .... 



who, ^ ** 
that. 



. . done ....*.... more .... which, 
. . given, rendered, ....*.... more ....** 
. . done ....*.... less ....**, 

irritated, incensed, old, ) 

another, injured, intimate, 
other, honest, innocent, 
ordinary, unkind. 



Insults, Harms, 
Wrongs, Slights, 
Offences, Things, 
Words .... spoken . 
Score o 

Things .... done . . 



• . . . . done ....*.... more . . 
. . irritated .... more ....**, 
. unknown .... more ....**, 



Injuries .... done ....*.... very ....**, 

88. It is that a full-grown man should a 

ghost he is 



Score 2 

inconceivable, 
improbable, 
impossible, 
unbelievable. 



/ while, 
\ when, if. 



* see unless, except, 

absurd, strange, . . . .fear **. . 

Score I 

best .... show .... that .... unafraid, 
foolish. . . .fear. . . .since. . . .grown, 
unwise. . . .become. . . .before, until,. . 
* . . . . believe .... story .... reading, 

Score o 

strange .... know .... when .... alone, 



(sane, 1 *** 
sober, ?• 
awake, j 
insane, drunk, 



said .... fear .... if . . wise, 
strange. . . .see. .**. .***, 
.dead, 
*. . . .be. . . .**. . . .dead. 



OTHER SENTENCES USED IN THIS STUDY 

3. I see man and the boy. 

Score 2 

the, 
Score I 

a, some, that, one, our, your, my, both the, the big, 
Score o 

big, this, 

9. Here is a man who do it. 

Score 2 

can, could, couldn't, can't, will, would, wouldn't, won't, may, 

cannot, might, should, shouldn't, does, must, doesn't. 
Score I 

did, shall, does not, likes to, ought to, saw him, dared to, 
Score o 

dared, never, always, will try to, 

10, The bird a song every morning. 

Score 2 

sings, sang, sung, 
Score I 

will sing, sing, has, warbles, chirps, pipes, sings us, gives, gives us. 
Score o 

likes, did, songs, song, 

13. Boys must be rude to mothers. 

Score 2 

(not, never,.)* .... their. 
Score I 

* . . . . good, dear, any, our, your, the. 
Score o 

*. . . . his, her, seldom, always, .... their, 

14. When the grows older he be a man. 

Score 2 

(boy, youth, lad,)* .... will. 
Score I 

may, must, can, shall, should, could, would, 
might, has to, is to, begins to, comes to, 
child, son, baby, brother, man, boys, .... will, 
Score 

* . . . . says, will, 

105 



lo6 Completion-Test Language Scales 

I5i The stars - brightly at 

Score 2 

(shine, shone, gleam, twinkle,)* .... night. 
Score I 

midnight, evening, seven, last, us, me, 
you, him, home, 7:30, 8 o'clock, 
shines, appear, look, show, sparkle. 



come out, were shining, j ■ ■ ■ ■ g , 

Score 

shining, are, .... night, *. . . . the sky, the town, city, 

17. The wind the dust into our eyes. 

Score 2 

blows, blew, blowed, sweeps, swept. 
Score I 

throws, carried, gets, sends, chases, carries, raises, brings, puts, 

threw, got, brought, sent, chased, raised, will blow, put, is blowing. 
Score 

draws, makes, has, flew, 

20. The little and his dog running a race. 

Score 2 

(boy, fellow, lad,)* .... (are, were, began,)** 
Score I 

*. . . .came, went, kept, try, play, like, won, was, is, 

child, master, man, ....**, came, went, etc. 
Score 

girl ....**, cat ....**, *.... had, 

26. Boys who play mud get their hands 



Score 2 

in .... the .... (dirty, soiled, muddy,)** 
Score I 

in .... the .... black, wet, sticky, filthy, nasty, 

in, around, .... wet, dirty, soft, black, any, with, near, ....**, 

marbles, games, ball, .... in, with, ....**, 

with dirt, in dirt, .... and ....**, at ... . moulding ....** 
Score 

in, with dirty, soft, .... dusty, , much, .... in .... **, 

39. If a person injures one by , without having intended 

any , one should insulted. 

Score 2 

accident, chance, | f injury, offence, J 

carelessness, j- * . . . . ^j harm, disrespect, 

thoughtlessness, J [ insult, affront, 

/ not, 1 ^^^ r be, feel, \ ♦** 

\ never, J • • • • | become, 



Appendix 



107 



Score I 

mistake, words, remarks, talking, gossip, 
fooling, unthoughtfulness, mishap, talk, 
speaking, fun, ignorance, anything, word, 
speech, something, haughtiness, shoving, 
pushing, hitting, joking, jokes. 



accident . 



. ***. . . .get, act, 
.accident. . . .***. 



* ' 



wrong, thing, unkindness, hurt, 
mischief, malice, mishap, trouble, 
Score o 

slander, insulting, snubbing, shooting, slapping. 



** *** 



40. A shelter the weather is appreciated on a 

day. 

Score 2 

greatly, thoroughly, 
fully, heartily, duly, 
certainly, usually, 
highly, always, 
generally, truly, 
indeed, much, keenly, 



frofn. 



stormy, ramy, 
snowy, wintry, 
cold, bad, hot, 



rarely, not, seldom, 



pleasant, beautiful, bright, 



from 

Score I 

{ only, surely, best, well, sincerely, ] 

from . . . . < most, fairly, quite, kindly, more, \ ....** 

[ better, often, to be, deeply, J 

from ....*.... damp, summer, wet, warm, against ....*. 

r I pretty, summer, sunny, warm, 

from .... not . . . . < , , ■ r 

\ good, clear, nice, nne. 

Score o 

from .... very, good, glad, not, ....**, to, in, for, of *. 



43. A home is merely a place one . 

live comfortably. 
Score 2 

(not, often, sometimes,)*. . . . where .... (may, can,)" 
Score I 

*. . . . in which, that, ....**, will, would, should, 

generally, usually, just, 

now, really, now never, 

*, generally, usually, etc for .... to, * .... so 

Score o 

* . . . . where .... does, * . . . . for .... who, 

but, only, always, .... where ....**, 



where 



io8 



Completion-Test Language Scales 



46 are times in the of almost of us 

when we for a long life. 



Score 2 






experience 



There. . s ,.\ 

[ history, 

There .... lives .... all 



nee, life, \ 
, career, J 



. everyone . 



J wish, hope, plan, 1 ** 
\ long, yearn, / 



Score I 

There ....*.... anyone, any, ....**, 

(seek, ask, pine, pray, 
look, prepare, fight, 
strive, suffer, 
*, youth, age, existence, 1 
days, past, midst, world, > .... all .. . 
minds, hearts, J 

There .... youth, age, etc everyone ....**, 

Score o 

There ....*.... everyone .... want, live, die. 

There ....*.... every ....**, 

there .... midst, heart, world, .... all .... are. 



47. Children should that after all nobody is 

to care much more their success than 

parents. 



Score 2 

learn, know, 
realize, see, 
understand, 
remember, note, 
recognize, feel. 



Score I 



likely, apt, 

supposed, able, 

inclined, wont, 

disposed, going, 

willing, expected, 

concerning, \ ^^^ , . 

o7 V *** their .... own, 
about, for, J 



their .... 



their 



dear, loving, fond, kind, 
two, good, devoted, 

*....**... .***. . . . do, will, both, are, .... their, 

appreciate, consider, 

find, think, believe, 

{liable, sure, ever, made, ready, 1 
bound, known, here, trying, there, \ . .*' 
about, anxious, obligated, needed, J 
Score 

say, insist, ....**....***.... their .... own, 
*. . . . absolutely . . . .***. . . . their .... own, 



own, 



'. .their, .own, 



Appendix 109 

49. One's real appears often in his 

than in his speech. 

Score 2 

self, character, nature, 

intention, desire, ambition, [ actions, deeds, ] ** 

attitude, spirit, feeling, * . . more . . j conduct, habits, [ 

worth, disposition, patriotism, [ manner, behavior, J 

happiness, motive, 

Score I 

{ appearance, face, expression, tone, 1 

* . . . . more ....•{ manners, acts, letters, eyes, looks, \ 

\ silence, ways, thoughts, habits, J 

ability, power, 1 . - , , 

^, , ^ . > . . . . more .... writmg, letters, work, 

thought, meamng, J 

sense, life, manner, tact, ability, \ 

training, breeding, thought, education, ^ . . . . more ....**, 

object, soul, traits, effort, dignity, J 

Score o 

customs, minds, brain, friend, idea, .... more ....**, 

mind, nature, dream, dress, 

heart, doings, character, 
*. . . . most .... manners, thought .... more .... character, 

50. When two persons about which neither 

understands, they almost to disagree. 

Score 2 

that, \ -K-if j sure, ^ *** 



(talk, converse,)* .... , . ,- . . . ^^^ . . . ^ 

[ somethmg, J (^ certam, 

*....**.... seem .... always, 

Score I 

*....**.... are .... bound, positive, ready, willing, apt, liable, 

decide, ask, are talking, 



dispute, argue, speak, ' 
* . . . . things, matters, anything, objects, a subject, .... are . . . ***, 
*....**.... usually, will, .... have, 
*....**.... can .... conclude, agree. 
Score 

*....**.... are .... fit, always, very sure, 
fight, think, talking, ....**.... are .... ***, 
are .... something .... are .... ready, 

62. Sleep both and body. 

Score 2 

(refreshes, aids, helps, strengthens, improves,)* .... mind, 
Score I 

*, rests, stimulates, rebuilds, .... heart, brain, brains, eyes, health, 

makes .... health, mind, strength, builds .... mind, 
Score o 

rests .... legs, muscles, 



no Co7npletion-Test Language Scales 

68. The of your and mother is your brother. 

Score 2 

son .... father, 
Score I 

pleasure, pride, boy, child, support, love, care, children, .... father, 
Score o 

boy, reason, .... family, girl, work, .... father, 

69. It is hard keep getting on a 

rainy day. 
Score 2 

to .... from .... (wet, damp, cross, gloomy, drowsy,)* 
Score I 

c J tired, angry, sulky, dirty, sick, 

' ' ' ' \ out, dull, lazy, fretful, 
to .... busy .... ready, to ... . dry .... out, to ... . not .... * 
to .... on .... work, umbrellas, cold, wet. 
Score o 

to .... from .... asleep, home, to .... dry .... shelter, 

72 and rain plants 

Score 2 

(Sunshine, Sun,)* .... make .... (grow, thrive,)** 
*. . . . help, refresh, .... greatly. 

Score I 

Heat, Fertilizer, Sun, .... give .... nourishment, growth, 
*. . . . help .... along, *. . . . our .... need, *. . . . makes. .**, 
Air .... do ... . good, *. . . . make. . . .healthy, *. . . . the. .get, 
Water, Light .... helps, .... grow, *. . . . keep .... growing. 
Snow .... gives .... food. Snow, Hail .... make .... grow, 

Score 

Ground .... kill .... growing, 

74. The boy has book. 

Score 2 

a, the, his, her, my, their. 
Score I 

a good, a big, a school, a nice, an, some, 
Score o 

pretty, red heavy, 

71. I like to go to 

Score 2 

school, church, play, bed. 
Score I 

see. 
Score o 

bad, today. 



Appendix 1 1 1 

80. A reasonable __ of sleep and rest is in order 

to a high of efficiency. 

Score 2 

I necessary, imperative, \ ^ / maintain, attain, 
' ' \ essential, desirable, J ' \ achieve, reach, 

.... degree, 
amount ....*.... (have, hold, keep,)*** .... standard, 
Score I 

amount .... desirable .... give .... degree, 

amount best ....**.... degree, 

amount ....*.... have, gain, secure, .... standing, amount, quality, 
amount ....*.... make, keep, hold, .... grade, state, 
amount ....*.... ***. . . . position. 
Score 

amount .... best .... do .... piece, 

81. The is always shining, storm-clouds 

sometimes — it us. 

Score 2 

Sun .... (but, although,)* .... (hide, obscure,)** .... from, 
Score I 

Sun .... the ....**.... from. 

Sun .... the .... reveal .... to. 

Sun ....*.... shield, bar, separate, cover, darken, .... from. 

Sun ....*.... cover .... and. 
Score o 

Sun .... and ....**.... to, 

85. The least difficult — are by no _ always the 

most , are the tasks 

the most disagreeable. 

Score 2 

J ' , . > *. . .means. . .pleasant. . .nor. . .hardest. . . always, 
undertakings J 

Score I 

* . . . . means .... profitable, trifling, .... nor .... hardest .... always, 
*. . . . means .... profitable .... nor .... profitable .... always. 

Score 

* . . . . means .... pleasing .... altho .... hard .... always, 

94. When one angry he should forth an 

effort his actions. 

Score 2 

is .... put .... to .... (control, restrain, check, curb)* 



112 Completion-Test Language Scales 

Score I 

( subdue, overcome, crush, calm, change, cure, 

is. . . .put. . . .to. . . . \ conquer, push, prevent, guard, hide, stop, 
[ consider, conceal, 

is .... bring, take, set .... to ....*, 

is .... bring .... to .... overcome, subdue, 
Score 

is .... set .... to .... maintain, 

is .... bring .... to ... . conceal, 

is .... try .... and .... stop, 

96 want are often caused by 

Score 2 

„ ^ ,1 drink, ignorance, laziness, \ * 

Poverty .... and \ • ^ j,- , ( 

\ sickness, disease, neglect J 

Score I 

Times .... of .... famine, 

Cases .... of ....*, 

Things . . . people . . . selfishness, jealousy, indulgence, imagination, 

Need .... and .... pleasure, 

People .... in ....*, 

What .... girls .... variety. 
Score 

Health .... and .... laziness. Horrors .... of ... . obstinacy. 

Hunger .... and .... cries. Conditions .... in ... . neglect, 

98. Children to pick 

Score 2 

like .... (flowers, berries, apples, fruit, daisies)* 
Score I 

come, are, came, are not, go, likes, 

went, try, were, wish, have, ought 

climb, jump apples, like .... flower, nuts, 

try .... quarrels, playmates, 
Score 

go .... stick, 

99. All animals shelter during a 

Score 2 

(seek, hunt, like, want, need, require,)* .... storm, 

* . . . . shower, rain. 
Score I 

find, have, take, get, love, look for .... night, shower, rain, 

* . . . . winter, need .... day. 
Score 

are, will, do ... . storm, have, shall .... year, day, summer. 



Appendix 



113 



to dumb ... 

(kind, good)** . . . (animals, persons)*** 



pats .... pleasant . . . 

. ***, signs .... best 
*** 



often 
. used 



animals, 
. . persons, 



. animals, 
. people. 



100. Sympathetic are 

Score 2 

people, boys, 1 

men, girls, women, \* . ■ 

persons, children, J 
Score I 

*....**.... ones, friends, 

characters, friends, ....**. 

persons .... sympathetic . 

words .... kind, nothing,. . . .animals, 

feelings, hearts, .... shown .... ***, 
Score o 

things, actions ....**.... ***, people ... 

children .... not .... to learn, forms . . . 

always .... good .... people, 

loi. A boy - run than a 

Score 2 

can, will, may)*. ... (further, better, faster)" 

can .... more .... mile. 
Score I 

cannot .... faster .... horse, 

likes to .... better, more, .... girl, man, 

could, should, ....**.... ***, should, has, can't, . . . more . . . mile, 

*, could, should, .... quicker, sooner, more, swifter, .... ***, 

can .... faster .... snail, cat, rat, dog, always . . . faster . . . girl, 

can, would, .... rather, sooner, oftener, .... girl, 

will, can, should ....**.... man. 
Score 

can .... fast .... man, took .... and . . . jump, 

who . . . more .... mile, 

102. A drink is very refreshing to a who is 



.(baby, girl)^ 



Score 2 




r thirsty, hot, ill, 
j tired, working, 
sick, traveling, 
exhausted, warm, 



person, laborer, 
men, runner, 
•j woman, girl, 
child, tramp, 
boy, workmen. 
Score I 

healthy, soft, common, little, fine, water, 

beer, whiskey, soda, 5 cent, clean, 

*. . . . man, girl, boy .... healthy, well, here, running, 

* . . . . dog .... ***, 

little, small boy ***, * ** dry, 

Score o 

fine .... man .... good. 



114 Completion-Test Language Scales 

103. A joke one's self is seldom thoroughly 

Score 2 

(on, upon, about)* .... appreciated, enjoyed, 
Score I 

^ \ pleasant, told, seen, played, known, reasonable, good, 

' ' ' ' \ funny, explained, expressed, kept, likes, 

to, with .... funny, by .... amusing, 
Score o 

about .... queer, in, of .... finished, with, in .... true, good^ 

104. One feels inclined to work it is 

Score 2 

(little, less)* .... (when, if,)** .... (hot, warm)*** 

much, more, ....**.... cold, cool, 
Score I 

* . . . . after .... dark, * ....**.... winter, nice, 

very ....**.... interesting, 

dis, not, ] 

seldom, \ .... while, **,.... hot, 

himself, J 

seldom, really, rather, ....**.... necessary, 

himself, 1 ** ^. . , often ....**.... raining,, 

, >...**... time, important, - , , 

much, J I r- . jjQ^ ... .for .... hard, 

well. ...**... .easy, much . . . though . . .hard. 

Score 

so, too, very, almost, it, .... when .... hot, day, 

105. Brothers — sisters should always to help 

other. 

Score 2 

J f try, offer, strive, aim, endeavor, learn, seek, 1 ^ , 

" ' ' \ consent, want, attempt, wish, like, agree, / ' 

Score I 

and .... have, go, hurry, stay, love, work, be ready, come, . . .each, 
and ....*.... one, an, the, one, some, one an, 
and .... ask .... each, 

Score 

and ....*.... out, along, and .... agree .... an, 
and .... go .... the, and .... glad .... each, 

106. Birds have which enable them to through 

the 

Score 2 

air, woods, streets, sky, \ * 



^ clouds, country, meadows. 



Appendix 



115 



Score I 

wings .... go ....*, wind, world, food .... eat .... winter, 
wing, foods, .... fly ....*, nests .... sleep, rest, .... night, 
beaks .... pick .... summer, feathers .... fly ....*, 
power .... fly ....*, feathers .... live .... winter, cold, 
wings, .... fly .... place, 

Score o 

instincts, trees .... live .... year, that .... go .... air, 
incense .... wander .... world, homes .... fly .... winter, 



107. the weather is .. 

than when it is 



one should wear heavier 



Score 2 

(When, If)*., (cold, cool)**.. 
Score I 



clothing, clothes, 
garments, cloaks, 
coats, wraps, 
underwear, 



J hot. 



' I warm, 



*. . . . stormy . 
cold .... when 

* . . . . winter .... *** . . 

Although ....**.... *** . 

Score 

How .... no ... .***. . 
Like .... today .... *** 

Here, Sometimes ....**. 



. warmer, good, nice, 
. ***. . . . nice, hot. 



summer, * . . . . bad .... *** .... ***, 
. ***, As, Now, ...**.. .clothes ...***, 



cold, 
***^ Tho. . . .warm. . . .***. . . ***^ 



108. One cannot his thoroughly he 

has good teeth. 

Score 2 

(chew, masticate, grind, bite)* .... food (unless, until)**, 

Score I 

eat .... food, meals, supper ....**, do ... . work ....**, 
have .... health .... unless, spoil .... looks .... when, if, 
* . . . . food .... without, maintain .... health .... unless. 

Score o 

eat, chew, .... food .... when, if, because, though, 

clean .... teeth .... when, keep .... teeth clean, unless, 

have .... way .... till, 



3. CALCULATION OF MEDIAN SCORE IN LANGUAGE SCALES 

Each child who spends the allotted amount of time in an attempt to complete 
the sentences of any of the language scales described in this study should be 
given as a total score the sum of the number of points made upon the individual 
sentences contained in the scale. For example, the child who completes 
perfectly the first three sentences of Scale B, and almost perfectly the fourth 
sentence in this scale, should be given a total score of seven points on Scale B. 
(2+2+2 + 1=7.) 

To find the ability of the class, it will be necessary to take into consideration 
the total score made by each child in the class. A distribution should therefore 
be prepared showing the scores made by the individual members of the class. 
This distribution should indicate the number of pupils in the class who make 
a score of zero, the number making a score of one, the number making a score 
of two, the number making a score of three, and so on for each step up to 
twenty, the highest possible score in Scales B to E. As examples of this sort of 
distribution, we may take the following: 

Number of Times Each Score Was Made in Language Scale C 
Score 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 



Group X 
Group Y 
Group Z 



3584322.1 

. .1.235643212 . . . . 
22354.6342 



There are 28 individuals in Group X, 29 individuals in Group Y, and 
32 individuals in Group Z. The only adequate comparison of these three 
groups is such a table as that shown above, or a surface of distribution repre- 
senting the same facts. The average score, or even the median score, is in 
itself inadequate as a measure of the group, although it is usually desirable to 
calculate the median as an indication of the central tendency of the group's 
ability. 

The median of any distribution is that point on the scale which divides the 
distribution into two exactly equal parts. When the scales are very crude, 
and measurements of small numbers of individuals are being considered, it is 
not worth while to locate the median point any more accurately than by indi- 
cating upon what step of the scale it falls. In the case of carefully derived 
scales, however, it is often desirable, especially where the group to be measured 
is reasonably large, to locate the exact point within the step where the median 
falls. This median point in the case of the scales here presented may well be 
calculated to the tenth, or even to the hundredth of a unit, if 200 or more 
individuals are in the group being measured. 

Since there are 28 individuals in Group X of the distributions shown above, 
the median point will evidently fall between the fourteenth and the fifteenth 
individuals. If we begin with the three individuals making a score of 2, and 
116 



Appendix 117 

count up through the five individuals making a score of 3, we should have 
to count out six of the eight individuals making a score of 4 in order to 
arrive at the point upon each side of which an equal number (14) of papers 
were scored. 

It now becomes necessary to define the fourth step. Some of those scored 
four may have been worth just barely 4 points, while others of this group 
may have been worth almost 5 points. It is impossible, of course, to know 
at just what points between these two extremes each of the eight individuals 
was located. The best single assumption to make, and the one which should 
always be made, is that those individuals scoring upon any single step of a 
scale are distributed along the step at equal distances from each other. We 
may therefore assume that the eight individuals scored upon step 4 range 
from 4.0 to 4.999 and lie at equal distances from each other along this range. 

If we count out six, therefore, of the eight individuals who scored on step 4, 
we shall arrive at a point which is approximately 4.7. 4.7 is therefore the 
median point of Group X. 

Similarly there are 29 individuals in Group Y. The middle case is the fifteenth 
individual, who is the fourth of the six scored on step 9. This individual has 
fourteen persons scored above him in ability and fourteen persons scored 
below him in ability. The median point, therefore, will lie at the middle of 
that fraction of the step assigned to him. In order to reach this point it will 
be necessary to count out three and a half of the six individuals scored on step 9, 
which brings us to 9.6, the median of Group Y. 

Group Z presents a peculiar problem in the calculation of its median. There 
are 16 individuals above score 14, and 16 individuals below score 14. Probably 
the wisest assumption to make is that the four individuals scored on 13 take up 
all of the thirteenth step and that the six individuals scored upon 15 take up 
all of that step. If this is assumed, the median falls upon step 14, probably 
at 14.5, since any given distance on a scale is best represented by its middle 
point. 

The 25 percentile and the 75 percentile are to be found in a manner similar 
to that for finding the median, counting into the distribution one-fourth of the 
total number of cases for the first, and three-fourths of the total number of 
cases for the second. 



4. TENTATIVE STANDARD SCORES IN LANGUAGE SCALES 
B, C, D, AND E 

The new scales proposed in this monograph have not as yet been employed 
upon a sufficiently large number of children in each grade to establish any 
definite standards of attainment. Although each sentence has been well tested 
in other combinations, the scores that will be obtained with the new scales can 
only be estimated. It seems worth while, however, especially for Scales B, 
C, D, and E, which will probably be employed somewhat more generally than 
the four special-type scales, to indicate in a general way what results may be 
expected in each school grade. The writer therefore gives below the best esti- 



Ii8 Completion-Test Language Scales 

matei he is able to make of the median score that any given school grade should 
make on one of these four scales. 



Grade 


Medi; 


II 


3-0 


III 


6.0 


IV 


8.0 


V 


9.6 


VI 


II. o 


VII 


12.3 


VIII 


13-3 


IX 


14.2 


X 


153 


XI 


15-8 


XII 


16.2 



The above tentative standards will not be found to be exact for any given 
scale, but until we have accurate results from a large number of applications 
of each scale in each grade, the above figures may be used as the best estimate 
available for any one of the four scales. On the whole it may be said that the 
above estimates are more likely to be too low than to be too high. One may 
also expect the same class or classes of equal ability to make a median score 
from .4 to .8 of a point lower in Scale C than in Scale B, while the median 
on either Scale D or Scale E will probably fall between that obtained on 
Scale B and that obtained on Scale C. 

With a view to establishing more accurate standards of attainment, the 
writer will be pleased to receive copies of the results obtained by any investi- 
gator employing any of the scales proposed in this monograph. If anyone, 
having five hundred or more public school pupils to measure, is willing to 
cooperate to the extent of reporting to the writer the score of each child on 
each sentence of the scale used, the writer will be glad to send him blanks for 
making such records and to refund 10 per cent of the purchase price of the 
scales (as purchased from the Teachers College Bureau of Publications) imme- 
diately upon receipt of such reports. 



1 In making this estimate it is of course assumed that anyone who wishes to compare their 
results with these figures will make the tests carefully as directed on pages 20 to 22 of this 
monograph, employing the blanks furnished by the Teachers College Bureau of Publications, 
and scoring each sentence according to the scheme given in Section 2 of this Appendix. Any 
deviations from this procedure should not be made without making allowances for differences 
in the results. 



